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dbr:Timeline_of_number_theory	dbo:wikiPageWikiLink	dbr:Combinatorics .
dbr:Levi_graph	dbo:wikiPageWikiLink	dbr:Combinatorics .
dbr:Haim_Hanani	dbo:wikiPageWikiLink	dbr:Combinatorics .
<http://dbpedia.org/resource/R._M._Wilson__R._M._Wilson__1>	dbo:academicDiscipline	dbr:Combinatorics .
dbr:Separable_permutation	dbo:wikiPageWikiLink	dbr:Combinatorics .
dbr:Lagrange_inversion_theorem	dbo:wikiPageWikiLink	dbr:Combinatorics .
dbr:Independence_Theory_in_Combinatorics	dbo:wikiPageWikiLink	dbr:Combinatorics .
dbr:Combinatorial_matrix_theory	dbo:wikiPageWikiLink	dbr:Combinatorics .
dbr:Chip-firing_game	dbo:wikiPageWikiLink	dbr:Combinatorics .
dbr:Mathematics	dbo:wikiPageWikiLink	dbr:Combinatorics .
<http://dbpedia.org/resource/Field_(mathematics)>	dbo:wikiPageWikiLink	dbr:Combinatorics .
dbr:Finite_field	dbo:wikiPageWikiLink	dbr:Combinatorics .
dbr:Game_theory	dbo:wikiPageWikiLink	dbr:Combinatorics .
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@prefix rdfs:	<http://www.w3.org/2000/01/rdf-schema#> .
dbr:Combinatorics	rdfs:label	"Combinatoria"@it ,
		"\u03A3\u03C5\u03BD\u03B4\u03C5\u03B1\u03C3\u03C4\u03B9\u03BA\u03AE"@el ,
		"Kombinatorika"@cs ,
		"Combinatorics"@en ,
		"\uC870\uD569\uB860"@ko ,
		"\u7EC4\u5408\u6570\u5B66"@zh ,
		"Kombinatorik"@de ,
		"Konbinatoria"@eu ,
		"\u062A\u0631\u0643\u064A\u0628\u0627\u062A"@ar ,
		"Kombinatorik"@sv ,
		"\u041A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u0438\u043A\u0430"@ru ,
		"Kombinatoriko"@eo ,
		"Combinatoire"@fr ,
		"Combinat\u00F2ria"@ca ,
		"\u041A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u0438\u043A\u0430"@uk ,
		"Combinat\u00F3ria"@pt ,
		"\u7D44\u5408\u305B\u6570\u5B66"@ja ,
		"Combinatoria"@es ,
		"Combinatoriek"@nl ,
		"Kombinatoryka"@pl ,
		"Kombinatorika"@in ;
	rdfs:comment	"En math\u00E9matiques, la combinatoire, appel\u00E9e aussi analyse combinatoire, \u00E9tudie les configurations de collections finies d'objets ou les combinaisons d'ensembles finis, et les d\u00E9nombrements."@fr ,
		"Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. A mathematician who studies combinatorics is called a combinatorialist."@en ,
		"Kombinatoryka \u2013 dzia\u0142 matematyki, zajmuj\u0105cy si\u0119 badaniem struktur sko\u0144czonych lub niesko\u0144czonych, ale przeliczalnych. Np. okre\u015Blenie, ile jest podzbior\u00F3w k-elementowych w zbiorze n-elementowym stanowi jedno z typowych zagadnie\u0144 kombinatoryki. Nazwa dyscypliny pochodzi od G.W. Leibniza. Kombinatoryka sw\u00F3j rozw\u00F3j zawdzi\u0119cza rachunkowi prawdopodobie\u0144stwa, teorii graf\u00F3w, teorii informacji i innym dzia\u0142om matematyki stosowanej. Stanowi jeden z dzia\u0142\u00F3w matematyki dyskretnej."@pl ,
		"\uC870\uD569\uB860(\u7D44\u5408\u8AD6, \uC601\uC5B4: combinatorics) \uB610\uB294 \uC870\uD569\uC218\uD559(\u7D44\u5408\u6578\u5B78)\uC740 \uC720\uD55C\uD558\uAC70\uB098 \uAC00\uC0B0\uC801\uC778 \uAD6C\uC870\uB4E4\uC5D0 \uB300\uD558\uC5EC, \uC5B4\uB5A4 \uC8FC\uC5B4\uC9C4 \uC131\uC9C8\uC744 \uB9CC\uC871\uC2DC\uD0A4\uB294 \uAC83\uB4E4\uC758 \uAC00\uC9D3\uC218\uB098 \uC5B4\uB5A4 \uC8FC\uC5B4\uC9C4 \uC131\uC9C8\uC744 \uADF9\uB300\uD654\uD558\uB294 \uAC83\uC744 \uC5F0\uAD6C\uD558\uB294 \uC218\uD559 \uBD84\uC57C\uC774\uB2E4."@ko ,
		"\u7D44\u5408\u305B\u6570\u5B66\uFF08\u304F\u307F\u3042\u308F\u305B\u3059\u3046\u304C\u304F\u3001\u82F1\u8A9E: combinatorics\uFF09\u3042\u308B\u3044\u306F\u7D44\u5408\u305B\u8AD6\uFF08\u304F\u307F\u3042\u308F\u305B\u308D\u3093\uFF09\u3068\u306F\u3001\u7279\u5B9A\u306E\u6761\u4EF6\u3092\u6E80\u305F\u3059\uFF08\u666E\u901A\u306F\u6709\u9650\u306E\uFF09\u5BFE\u8C61\u304B\u3089\u306A\u308B\u96C6\u307E\u308A\u3092\u7814\u7A76\u3059\u308B\u6570\u5B66\u306E\u5206\u91CE\u3002\u96E2\u6563\u6570\u5B66\u306E\u4E2D\u6838\u306E\u4E00\u3064\u3068\u3055\u308C\u308B\u3002\u7279\u306B\u554F\u984C\u3068\u3055\u308C\u308B\u3053\u3068\u3068\u3057\u3066\u3001\u96C6\u5408\u306B\u5165\u3063\u3066\u3044\u308B\u5BFE\u8C61\u3092\u6570\u3048\u305F\u308A\uFF08\u6570\u3048\u4E0A\u3052\u7684\u7D44\u5408\u305B\u8AD6\uFF09\u3001\u3044\u3064\u6761\u4EF6\u304C\u6E80\u305F\u3055\u308C\u308B\u306E\u304B\u3092\u5224\u5B9A\u3057\u3001\u305D\u306E\u6761\u4EF6\u3092\u6E80\u305F\u3057\u3066\u3044\u308B\u5BFE\u8C61\u3092\u69CB\u6210\u3057\u305F\u308A\u89E3\u6790\u3057\u305F\u308A\uFF08\u7D44\u5408\u305B\u30C7\u30B6\u30A4\u30F3\u3084\u30DE\u30C8\u30ED\u30A4\u30C9\u7406\u8AD6\uFF09\u3001\u300C\u6700\u5927\u300D\u300C\u6700\u5C0F\u300D\u300C\u6700\u9069\u300D\u306A\u5BFE\u8C61\u3092\u307F\u3064\u3051\u305F\u308A\uFF08\u6975\u5024\u7D44\u5408\u305B\u8AD6\u3084\u7D44\u5408\u305B\u6700\u9069\u5316\uFF09\u3001\u305D\u308C\u3089\u306E\u5BFE\u8C61\u304C\u6301\u3061\u3046\u308B\u4EE3\u6570\u7684\u69CB\u9020\u3092\u307F\u3064\u3051\u305F\u308A\uFF08\u4EE3\u6570\u7684\u7D44\u5408\u305B\u8AD6\uFF09\u3059\u308B\u3053\u3068\u304C\u6319\u3052\u3089\u308C\u308B\u3002"@ja ,
		"Konbinatoria kontaketa-ebazkizunak aztertzen dituzten teknika matematikoen multzoa da. Zehatzago, konbinatoria multzo finituen kardinalen inguruko propietate eta ezaugarriak aztertzen arduratzen da, propietate berdinak dituzten elementuak zenbatu eta hauen arteko eraikuntzak ikasten dituelarik. Konbinatoria aljebra abstraktuan, geometrian, grafo teorian eta probabilitateen kalkuluan erabiltzen da. Praktikan, informatikan eta ikerketa operatiboan aplikazio zuzenak ditu."@eu ,
		"Kombinatorika adalah cabang matematika yang membahas sifat-sifat dan cara menghitung struktur-struktur terhingga. Kombinatorika berkaitan erat dengan cabang-cabang matematika lain, dan memiliki banyak penerapan di ilmu logika sampai biologi evolusioner sampai ilmu komputer. Dalam matematika murni, permasalahan kombinatorika banyak ditemukan khususnya di aljabar, teori peluang, topologi, geometri, dan bidang-bidang terapannya. Walaupun berfokus pada sistem hingga, beberapa permasalahan dan teknik kombinatorika dapat diperumum ke bentuk tak hingga (yang diskret dan terhitung)."@in ,
		"Kombinatorik \u00E4r den gren av matematiken som studerar kombinationer, permutationer och uppr\u00E4kningar av element i m\u00E4ngder och de relationer som karakteriserar dessas egenskaper. Metoderna f\u00F6r detta \u00E4r grundl\u00E4ggande i den diskreta matematiken. F\u00F6reg\u00E5ngsm\u00E4n inom omr\u00E5det \u00E4r bland andra Blaise Pascal, Pierre de Fermat, Pierre R\u00E9mond de Montmort, James Stirling och br\u00F6derna Jacob och Johann Bernoulli."@sv ,
		"Con il termine combinatoria o combinatorica (che comprende anche la geometria combinatoria) si intende il settore della matematica che studia insiemi finiti di oggetti semplici (interi, stringhe, nodi e collegamenti, punti e linee, configurazioni discrete, insiemi finiti, ...) che soddisfano propriet\u00E0 ben definite e tendenzialmente semplici."@it ,
		"\u0627\u0644\u062A\u0631\u0643\u064A\u0628\u0627\u062A \u0623\u0648 \u0627\u0644\u062A\u0648\u0627\u0641\u0642\u064A\u0627\u062A (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Combinatorics)\u200F \u0647\u064A \u0623\u062D\u062F \u0641\u0631\u0648\u0639 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0627\u0644\u062A\u064A \u062A\u062F\u0631\u0633 \u0627\u0644\u0628\u064F\u0646\u0649 \u0627\u0644\u0645\u062A\u0642\u0637\u0639\u0629 \u0627\u0644\u0645\u0646\u062A\u0647\u064A\u0629 \u0648\u0627\u0644\u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u0639\u062F. \u062A\u062A\u0636\u0645\u0646 \u0627\u0644\u062A\u0631\u0643\u064A\u0628\u0627\u062A \u0639\u062F\u0651 \u0627\u0644\u0639\u0646\u0627\u0635\u0631 \u0641\u064A \u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0627\u062A\u060C \u0645\u0639 \u062A\u062D\u062F\u064A\u062F \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062A \u062A\u062A\u0648\u0627\u0641\u0642 \u0645\u0639 \u0627\u0644\u0645\u0639\u0627\u064A\u064A\u0631 \u0627\u0644\u0645\u0637\u0644\u0648\u0628\u0629\u060C \u0648\u0643\u0630\u0644\u0643 \u062F\u0631\u0627\u0633\u0629 \u0628\u0646\u0627\u0621 \u0648\u062A\u062D\u0644\u064A\u0644 \u0627\u0644\u0643\u0627\u0626\u0646\u0627\u062A \u0627\u0644\u062A\u064A \u062A\u062D\u0642\u0642 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u064A\u064A\u0631 (\u0643\u0645\u0627 \u0641\u064A \u0648\u0646\u0638\u0631\u064A\u0629 )\u060C \u064A\u0647\u062A\u0645 \u0647\u0630\u0627 \u0627\u0644\u0639\u0644\u0645 \u0623\u064A\u0636\u0627\u064B \u0628\u0625\u064A\u062C\u0627\u062F \u0627\u0644\u0643\u0627\u0626\u0646\u0627\u062A \u0627\u0644\u0623\u0643\u0628\u0631 \u0623\u0648 \u0627\u0644\u0623\u0635\u063A\u0631 \u0623\u0648 \u0627\u0644\u0623\u0641\u0636\u0644 (\u0641\u064A\u0645\u0627 \u064A\u0639\u0631\u0641 \u0648\u0627\u0644\u062A\u0648\u0627\u0641\u0642\u064A\u0627\u062A \u0627\u0644\u062A\u062D\u0633\u064A\u0646\u064A\u0629). \u0648\u062F\u0631\u0627\u0633\u0629 \u0627\u0644\u0647\u064A\u0643\u0644 \u0627\u0644\u062A\u0631\u0643\u064A\u0628\u064A \u0627\u0644\u0638\u0627\u0647\u0631 \u0641\u064A \u0645\u062D\u062A\u0648\u0649 \u062C\u0628\u0631\u064A\u060C \u0623\u0648 \u062A\u0637\u0628\u064A\u0642 \u062A\u0642\u0646\u064A\u0627\u062A \u0627\u0644\u062C\u0628\u0631 \u0644\u062D\u0644 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u062A\u0631\u0643\u064A\u0628\u0627\u062A."@ar ,
		"Die Kombinatorik ist eine Teildisziplin der Mathematik, die sich mit endlichen oder abz\u00E4hlbar unendlichen diskreten Strukturen besch\u00E4ftigt und deshalb auch dem Oberbegriff diskrete Mathematik zugerechnet wird. Beispiele sind Graphen (Graphentheorie), teilgeordnete Mengen wie Verb\u00E4nde, Matroide, kombinatorische Designs, lateinische Quadrate, Parkettierungen, Permutationen von Objekten, Partitionen. Die Abgrenzung zu anderen Teilgebieten der diskreten Mathematik ist flie\u00DFend. Eine Definition von George P\u00F3lya bezeichnet die Kombinatorik als Untersuchung des Abz\u00E4hlens, der Existenz und Konstruktion von Konfigurationen."@de ,
		"A combinat\u00F3ria \u00E9 um ramo da matem\u00E1tica que estuda cole\u00E7\u00F5es finitas de elementos que satisfazem crit\u00E9rios espec\u00EDficos determinados e se preocupa, em particular, com a \"contagem\" de elementos nessas cole\u00E7\u00F5es (combinat\u00F3ria enumerativa), com decidir se certo objeto \"\u00F3timo\" existe (combinat\u00F3ria extremal) e com estruturas \"alg\u00E9bricas\" que esses objetos possam ter (combinat\u00F3ria alg\u00E9brica). Um exemplo de problema combinat\u00F3rio \u00E9 o seguinte: Quantas ordena\u00E7\u00F5es \u00E9 poss\u00EDvel fazer com um baralho de 52 cartas?"@pt ,
		"La combinatoria es una rama de la matem\u00E1tica perteneciente al \u00E1rea de matem\u00E1ticas discretas que estudia la enumeraci\u00F3n, construcci\u00F3n y existencia de propiedades de configuraciones que satisfacen ciertas condiciones establecidas. Adem\u00E1s, estudia las ordenaciones o agrupaciones de un determinado n\u00FAmero de elementos."@es ,
		"Kombinatoriko estas bran\u0109o de la matematiko, en kiu oni studas la ekziston kaj konstruon de diversaj kaj de elementoj la\u016D difinitaj reguloj, kaj ser\u0109as la nombrojn da kombinoj kaj aran\u011Doj de diversaj tipoj. La gravan rolon en la evoluo de kombinatoraj metodoj plenumis Gottfried Wilhelm Leibniz, Jakob Bernoulli kaj Leonhard Euler. De la 50-aj jaroj de la 20-a jarcento intereso pri kombinatoriko revivi\u011Das pro la impeta evoluo de komputiko, cibernetiko, diskreta matematiko, kaj informteorio. La \u0109efaj konceptoj de kombinatoriko estas:"@eo ,
		"La combinat\u00F2ria \u00E9s una branca de les matem\u00E0tiques pures que s'ocupa de l'estudi d'objectes discrets (i normalment tamb\u00E9 finits). Una part de la combinat\u00F2ria inclou el \"comptar\" el nombre d'objectes que satisfan un criteri (combinat\u00F2ria enumerativa), decidir quan aquest criteri es compleix, i construir i analitzar els objectes que compleixen el criteri. Una de les \u00E0rees m\u00E9s antiga i m\u00E9s accessible de la combinat\u00F2ria \u00E9s la teoria de grafs."@ca ,
		"Combinatoriek of combinatieleer is een tak van de wiskunde. In de combinatoriek bestudeert men eindige verzamelingen van objecten die aan gespecificeerde eigenschappen voldoen. In het bijzonder houdt men zich bezig met het \"tellen\" van objecten in deze verzamelingen en het bepalen of er zekere \"optimale\" objecten in een verzameling aanwezig zijn. Aangezien combinatoriek vooral over tellen gaat, wordt het wel de \"kunst van het tellen\" genoemd."@nl ,
		"\u0397 \u03C3\u03C5\u03BD\u03B4\u03C5\u03B1\u03C3\u03C4\u03B9\u03BA\u03AE \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BA\u03BB\u03AC\u03B4\u03BF\u03C2 \u03C4\u03C9\u03BD \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03CE\u03BD \u03C0\u03BF\u03C5 \u03B1\u03C3\u03C7\u03BF\u03BB\u03B5\u03AF\u03C4\u03B1\u03B9 \u03BC\u03B5 \u03C4\u03B7 \u03BC\u03B5\u03BB\u03AD\u03C4\u03B7 \u03C4\u03C9\u03BD \u03C0\u03B5\u03C0\u03B5\u03C1\u03B1\u03C3\u03BC\u03AD\u03BD\u03C9\u03BD \u03BA\u03B1\u03B9 \u03C4\u03C9\u03BD \u03AC\u03C0\u03B5\u03B9\u03C1\u03C9\u03BD \u03B1\u03BB\u03BB\u03AC \u03BC\u03B5\u03C4\u03C1\u03AE\u03C3\u03B9\u03BC\u03C9\u03BD \u03B4\u03B9\u03B1\u03BA\u03C1\u03B9\u03C4\u03CE\u03BD . \u03A0\u03C4\u03C5\u03C7\u03AD\u03C2 \u03BC\u03B5 \u03C4\u03B9\u03C2 \u03BF\u03C0\u03BF\u03AF\u03B5\u03C2 \u03B1\u03C3\u03C7\u03BF\u03BB\u03B5\u03AF\u03C4\u03B1\u03B9 \u03B7 \u03C3\u03C5\u03BD\u03B4\u03C5\u03B1\u03C3\u03C4\u03B9\u03BA\u03AE \u03C0\u03B5\u03C1\u03B9\u03BB\u03B1\u03BC\u03B2\u03AC\u03BD\u03BF\u03C5\u03BD \u03C4\u03B7\u03BD \u03BA\u03B1\u03C4\u03B1\u03BC\u03AD\u03C4\u03C1\u03B7\u03C3\u03B7 \u03C4\u03C9\u03BD \u03B4\u03BF\u03BC\u03CE\u03BD \u03B5\u03BD\u03CC\u03C2 \u03B4\u03B5\u03B4\u03BF\u03BC\u03AD\u03BD\u03BF\u03C5 \u03B5\u03AF\u03B4\u03BF\u03C5\u03C2 \u03BA\u03B1\u03B9 \u03BC\u03B5\u03B3\u03AD\u03B8\u03BF\u03C5\u03C2, \u03C4\u03B7\u03BD \u03B1\u03C0\u03CC\u03C6\u03B1\u03C3\u03B7 \u03C0\u03CC\u03C4\u03B5 \u03BC\u03C0\u03BF\u03C1\u03BF\u03CD\u03BD \u03BD\u03B1 \u03C0\u03BB\u03B7\u03C1\u03BF\u03CD\u03BD \u03BF\u03C1\u03B9\u03C3\u03BC\u03AD\u03BD\u03B1 \u03BA\u03C1\u03B9\u03C4\u03AE\u03C1\u03B9\u03B1, \u03C4\u03B7\u03BD \u03BA\u03B1\u03C4\u03B1\u03C3\u03BA\u03B5\u03C5\u03AE \u03BA\u03B1\u03B9 \u03C4\u03B7\u03BD \u03B1\u03BD\u03AC\u03BB\u03C5\u03C3\u03B7 \u03C4\u03C9\u03BD \u03B1\u03BD\u03C4\u03B9\u03BA\u03B5\u03B9\u03BC\u03AD\u03BD\u03C9\u03BD \u03C0\u03BF\u03C5 \u03C0\u03BB\u03B7\u03C1\u03BF\u03CD\u03BD \u03C4\u03B1 \u03BA\u03C1\u03B9\u03C4\u03AE\u03C1\u03B9\u03B1(\u03CC\u03C0\u03C9\u03C2 \u03C4\u03B1 \u03BA\u03B1\u03B9 \u03C4\u03B7\u03BD ) \u03C4\u03B7\u03BD \u03B5\u03CD\u03C1\u03B5\u03C3\u03B7 \"\u03BC\u03B5\u03B3\u03B1\u03BB\u03CD\u03C4\u03B5\u03C1\u03BF\u03C5\", \"\u03BC\u03B9\u03BA\u03C1\u03CC\u03C4\u03B5\u03C1\u03BF\u03C5\" \u03AE \"\u03B2\u03AD\u03BB\u03C4\u03B9\u03C3\u03C4\u03BF\u03C5\" \u03B1\u03BD\u03C4\u03B9\u03BA\u03B5\u03B9\u03BC\u03AD\u03BD\u03BF\u03C5 ( \u03BA\u03B1\u03B9 ) \u03BA\u03B1\u03B9 \u03C4\u03B7\u03BD \u03BC\u03B5\u03BB\u03AD\u03C4\u03B7 \u03C3\u03C5\u03BD\u03B4\u03C5\u03B1\u03C3\u03C4\u03B9\u03BA\u03CE\u03BD \u03B4\u03BF\u03BC\u03CE\u03BD \u03C0\u03BF\u03C5 \u03C0\u03C1\u03BF\u03BA\u03CD\u03C0\u03C4\u03BF\u03C5\u03BD \u03C3\u03B5 \u03AD\u03BD\u03B1 \u03B1\u03BB\u03B3\u03B5\u03B2\u03C1\u03B9\u03BA\u03CC \u03C0\u03BB\u03B1\u03AF\u03C3\u03B9\u03BF \u03AE \u03B5\u03C1\u03C6\u03B1\u03BC\u03CC\u03B6\u03BF\u03BD\u03C4\u03B1\u03C2 \u03B1\u03BB\u03B3\u03B5\u03B2\u03C1\u03B9\u03BA\u03AD\u03C2 \u03C4\u03B5\u03C7\u03BD\u03B9\u03BA\u03AD\u03C2 \u03C3\u03B5 \u03C0\u03C1\u03BF\u03B2\u03BB\u03AE\u03BC\u03B1\u03C4\u03B1 \u03C3\u03C5\u03BD\u03B4\u03C5\u03B1\u03C3\u03C4\u03B9\u03BA\u03AE\u03C2."@el ,
		"\u5E7F\u4E49\u7684\u7EC4\u5408\u6570\u5B66\uFF08\u82F1\u8A9E\uFF1ACombinatorics\uFF09\u5C31\u662F\u79BB\u6563\u6570\u5B66\uFF0C\u72ED\u4E49\u7684\u7EC4\u5408\u6570\u5B66\u662F\u7EC4\u5408\u8BA1\u6570\u3001\u56FE\u8BBA\u3001\u4EE3\u6570\u7ED3\u6784\u3001\u6570\u7406\u903B\u8F91\u7B49\u7684\u603B\u79F0\u3002\u4F46\u8FD9\u53EA\u662F\u4E0D\u540C\u5B66\u8005\u5728\u53EB\u6CD5\u4E0A\u7684\u533A\u522B\u3002\u603B\u4E4B\uFF0C\u7EC4\u5408\u6570\u5B66\u662F\u4E00\u95E8\u7814\u7A76\u53EF\u6578\u6216\u79BB\u6563\u5BF9\u8C61\u7684\u79D1\u5B66\u3002\u968F\u7740\u8BA1\u7B97\u673A\u79D1\u5B66\u65E5\u76CA\u53D1\u5C55\uFF0C\u7EC4\u5408\u6570\u5B66\u7684\u91CD\u8981\u6027\u4E5F\u65E5\u6E10\u51F8\u663E\uFF0C\u56E0\u4E3A\u8BA1\u7B97\u673A\u79D1\u5B66\u7684\u6838\u5FC3\u5185\u5BB9\u662F\u4F7F\u7528\u7B97\u6CD5\u5904\u7406\u3002 \u72ED\u4E49\u7684\u7EC4\u5408\u6570\u5B66\u4E3B\u8981\u7814\u7A76\u6EE1\u8DB3\u4E00\u5B9A\u6761\u4EF6\u7684\u7EC4\u6001\uFF08\u4E5F\u79F0\u7EC4\u5408\u6A21\u578B\uFF09\u7684\u5B58\u5728\u3001\u8BA1\u6570\u4EE5\u53CA\u6784\u9020\u7B49\u65B9\u9762\u7684\u95EE\u9898\u3002\u7EC4\u5408\u6570\u5B66\u7684\u4E3B\u8981\u5185\u5BB9\u6709\u7EC4\u5408\u8BA1\u6570\u3001\u3001\u3001\u7EC4\u5408\u6700\u4F73\u5316\uFF08\uFF09\u7B49\u3002"@zh ,
		"\u041A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0301\u0440\u0438\u043A\u0430 \u2014 \u0440\u0430\u0437\u0434\u0435\u043B \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438, \u043F\u043E\u0441\u0432\u044F\u0449\u0451\u043D\u043D\u044B\u0439 \u0440\u0435\u0448\u0435\u043D\u0438\u044E \u0437\u0430\u0434\u0430\u0447, \u0441\u0432\u044F\u0437\u0430\u043D\u043D\u044B\u0445 \u0441 \u0432\u044B\u0431\u043E\u0440\u043E\u043C \u0438 \u0440\u0430\u0441\u043F\u043E\u043B\u043E\u0436\u0435\u043D\u0438\u0435\u043C \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u043E\u0432 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u043E\u0433\u043E (\u0447\u0430\u0449\u0435 \u0432\u0441\u0435\u0433\u043E \u043A\u043E\u043D\u0435\u0447\u043D\u043E\u0433\u043E) \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u0432 \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0438\u0438 \u0441 \u0437\u0430\u0434\u0430\u043D\u043D\u044B\u043C\u0438 \u043F\u0440\u0430\u0432\u0438\u043B\u0430\u043C\u0438. \u041A\u0430\u0436\u0434\u043E\u0435 \u0442\u0430\u043A\u043E\u0435 \u043F\u0440\u0430\u0432\u0438\u043B\u043E \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u044F\u0435\u0442 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u0443\u044E \u0432\u044B\u0431\u043E\u0440\u043A\u0443 \u0438\u0437 \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u043E\u0432 \u0438\u0441\u0445\u043E\u0434\u043D\u043E\u0433\u043E \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430, \u043A\u043E\u0442\u043E\u0440\u0430\u044F \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u043D\u043E\u0439 \u043A\u043E\u043D\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0435\u0439. \u041F\u0440\u043E\u0441\u0442\u0435\u0439\u0448\u0438\u043C\u0438 \u043F\u0440\u0438\u043C\u0435\u0440\u0430\u043C\u0438 \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u043D\u044B\u0445 \u043A\u043E\u043D\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0439 \u044F\u0432\u043B\u044F\u044E\u0442\u0441\u044F \u043F\u0435\u0440\u0435\u0441\u0442\u0430\u043D\u043E\u0432\u043A\u0438, \u0441\u043E\u0447\u0435\u0442\u0430\u043D\u0438\u044F \u0438 \u0440\u0430\u0437\u043C\u0435\u0449\u0435\u043D\u0438\u044F. \u0422\u0438\u043F\u0438\u0447\u043D\u044B\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u0438\u043A\u0438: \u0422\u0435\u0440\u043C\u0438\u043D \u00AB\u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u0438\u043A\u0430\u00BB \u0431\u044B\u043B \u0432\u0432\u0435\u0434\u0451\u043D \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u043E\u0431\u0438\u0445\u043E\u0434 \u0432 1666 \u0433\u043E\u0434\u0443 \u041B\u0435\u0439\u0431\u043D\u0438\u0446\u0435\u043C \u0432 \u0442\u0440\u0443\u0434\u0435 \u00AB\u0420\u0430\u0441\u0441\u0443\u0436\u0434\u0435\u043D\u0438\u044F \u043E \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u043D\u043E\u043C \u0438\u0441\u043A\u0443\u0441\u0441\u0442\u0432\u0435\u00BB."@ru ,
		"Kombinatorika (kombinatorick\u00E1 matematika) je \u010D\u00E1st matematiky zab\u00FDvaj\u00EDc\u00ED se kolekcemi prvk\u016F mno\u017Ein s definovanou vnit\u0159n\u00ED strukturou. Ot\u00E1zky, kter\u00E9 kombinatorika \u0159e\u0161\u00ED, se obvykle t\u00FDkaj\u00ED po\u010Dtu n\u011Bjak\u00FDch objekt\u016F (nebo skupin objekt\u016F) s definovanou strukturou, speci\u00E1ln\u011B (pokud po\u010Det m\u016F\u017Ee b\u00FDt nulov\u00FD) existenc\u00ED objektu s definovanou strukturou."@cs ,
		"\u041A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0301\u0440\u0438\u043A\u0430 (\u041A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u043D\u0438\u0439 \u0430\u043D\u0430\u043B\u0456\u0437) \u2014 \u0440\u043E\u0437\u0434\u0456\u043B \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438, \u043F\u0440\u0438\u0441\u0432\u044F\u0447\u0435\u043D\u0438\u0439 \u0440\u043E\u0437\u0432'\u044F\u0437\u0430\u043D\u043D\u044E \u0437\u0430\u0434\u0430\u0447 \u0432\u0438\u0431\u043E\u0440\u0443 \u0442\u0430 \u0440\u043E\u0437\u0442\u0430\u0448\u0443\u0432\u0430\u043D\u043D\u044F \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0456\u0432 \u0434\u0435\u044F\u043A\u043E\u0457, \u0437\u0430\u0437\u0432\u0438\u0447\u0430\u0439, \u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u043E\u0457 \u043C\u043D\u043E\u0436\u0438\u043D\u0438 \u0432\u0456\u0434\u043F\u043E\u0432\u0456\u0434\u043D\u043E \u0434\u043E \u0437\u0430\u0434\u0430\u043D\u0438\u0445 \u043F\u0440\u0430\u0432\u0438\u043B. \u041A\u043E\u0436\u043D\u0435 \u0442\u0430\u043A\u0435 \u043F\u0440\u0430\u0432\u0438\u043B\u043E \u0432\u0438\u0437\u043D\u0430\u0447\u0430\u0454 \u0441\u043F\u043E\u0441\u0456\u0431 \u043F\u043E\u0431\u0443\u0434\u043E\u0432\u0438 \u0434\u0435\u044F\u043A\u043E\u0457 \u043A\u043E\u043D\u0441\u0442\u0440\u0443\u043A\u0446\u0456\u0457 \u0456\u0437 \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0456\u0432 \u0432\u0438\u0445\u0456\u0434\u043D\u043E\u0457 \u043C\u043D\u043E\u0436\u0438\u043D\u0438, \u0449\u043E \u0437\u0432\u0435\u0442\u044C\u0441\u044F \u043A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u043D\u043E\u044E \u043A\u043E\u043D\u0444\u0456\u0433\u0443\u0440\u0430\u0446\u0456\u0454\u044E. \u0422\u043E\u043C\u0443 \u043D\u0430 \u043C\u0435\u0442\u0456 \u043A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u043D\u043E\u0433\u043E \u0430\u043D\u0430\u043B\u0456\u0437\u0443 \u0441\u0442\u043E\u0457\u0442\u044C \u0434\u043E\u0441\u043B\u0456\u0434\u0436\u0435\u043D\u043D\u044F \u043A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u043D\u0438\u0445 \u043A\u043E\u043D\u0444\u0456\u0433\u0443\u0440\u0430\u0446\u0456\u0439, \u0430\u043B\u0433\u043E\u0440\u0438\u0442\u043C\u0456\u0432 \u0457\u0445 \u043F\u043E\u0431\u0443\u0434\u043E\u0432\u0438, \u043E\u043F\u0442\u0438\u043C\u0456\u0437\u0430\u0446\u0456\u044F \u0442\u0430\u043A\u0438\u0445 \u0430\u043B\u0433\u043E\u0440\u0438\u0442\u043C\u0456\u0432, \u0430 \u0442\u0430\u043A\u043E\u0436 \u0440\u043E\u0437\u0432'\u044F\u0437\u0430\u043D\u043D\u044F \u0437\u0430\u0434\u0430\u0447 \u043F\u0435\u0440\u0435\u043B\u0456\u043A\u0443. \u041D\u0430\u0439\u043F\u0440\u043E\u0441\u0442\u0456\u0448\u0438\u043C\u0438 \u043F\u0440\u0438\u043A\u043B\u0430\u0434\u0430\u043C\u0438 \u043A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u043D\u0438\u0445 \u043A\u043E\u043D\u0444\u0456\u0433\u0443\u0440\u0430\u0446\u0456\u0439 \u0454 \u043F\u0435\u0440\u0435\u0441\u0442\u0430\u043D\u043E\u0432\u043A\u0438, \u0440\u043E\u0437\u043C\u0456\u0449\u0435\u043D\u043D\u044F, \u043A\u043E\u043C\u0431\u0456\u043D\u0430\u0446\u0456\u044F \u0442\u0430 \u0440\u043E\u0437\u0431\u0438\u0442\u0442\u044F."@uk ;
	owl:differentFrom	dbr:Combinatoriality ;
	foaf:depiction	<http://commons.wikimedia.org/wiki/Special:FilePath/Young_diagram_for_541_partition.svg> ,
		<http://commons.wikimedia.org/wiki/Special:FilePath/Icosahedron.svg> ,
		<http://commons.wikimedia.org/wiki/Special:FilePath/Morse-Thue_sequence.gif> ,
		<http://commons.wikimedia.org/wiki/Special:FilePath/Self_avoiding_walk.svg> ,
		<http://commons.wikimedia.org/wiki/Special:FilePath/Kissing-3d.png> ,
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		<http://commons.wikimedia.org/wiki/Special:FilePath/Hasse_diagram_of_powerset_of_3.svg> ,
		<http://commons.wikimedia.org/wiki/Special:FilePath/Catalan_4_leaves_binary_tree_example.svg> .
@prefix dct:	<http://purl.org/dc/terms/> .
@prefix dbc:	<http://dbpedia.org/resource/Category:> .
dbr:Combinatorics	dct:subject	dbc:Combinatorics ;
	dbo:abstract	"\u5E7F\u4E49\u7684\u7EC4\u5408\u6570\u5B66\uFF08\u82F1\u8A9E\uFF1ACombinatorics\uFF09\u5C31\u662F\u79BB\u6563\u6570\u5B66\uFF0C\u72ED\u4E49\u7684\u7EC4\u5408\u6570\u5B66\u662F\u7EC4\u5408\u8BA1\u6570\u3001\u56FE\u8BBA\u3001\u4EE3\u6570\u7ED3\u6784\u3001\u6570\u7406\u903B\u8F91\u7B49\u7684\u603B\u79F0\u3002\u4F46\u8FD9\u53EA\u662F\u4E0D\u540C\u5B66\u8005\u5728\u53EB\u6CD5\u4E0A\u7684\u533A\u522B\u3002\u603B\u4E4B\uFF0C\u7EC4\u5408\u6570\u5B66\u662F\u4E00\u95E8\u7814\u7A76\u53EF\u6578\u6216\u79BB\u6563\u5BF9\u8C61\u7684\u79D1\u5B66\u3002\u968F\u7740\u8BA1\u7B97\u673A\u79D1\u5B66\u65E5\u76CA\u53D1\u5C55\uFF0C\u7EC4\u5408\u6570\u5B66\u7684\u91CD\u8981\u6027\u4E5F\u65E5\u6E10\u51F8\u663E\uFF0C\u56E0\u4E3A\u8BA1\u7B97\u673A\u79D1\u5B66\u7684\u6838\u5FC3\u5185\u5BB9\u662F\u4F7F\u7528\u7B97\u6CD5\u5904\u7406\u3002 \u72ED\u4E49\u7684\u7EC4\u5408\u6570\u5B66\u4E3B\u8981\u7814\u7A76\u6EE1\u8DB3\u4E00\u5B9A\u6761\u4EF6\u7684\u7EC4\u6001\uFF08\u4E5F\u79F0\u7EC4\u5408\u6A21\u578B\uFF09\u7684\u5B58\u5728\u3001\u8BA1\u6570\u4EE5\u53CA\u6784\u9020\u7B49\u65B9\u9762\u7684\u95EE\u9898\u3002\u7EC4\u5408\u6570\u5B66\u7684\u4E3B\u8981\u5185\u5BB9\u6709\u7EC4\u5408\u8BA1\u6570\u3001\u3001\u3001\u7EC4\u5408\u6700\u4F73\u5316\uFF08\uFF09\u7B49\u3002"@zh ,
		"\u0397 \u03C3\u03C5\u03BD\u03B4\u03C5\u03B1\u03C3\u03C4\u03B9\u03BA\u03AE \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BA\u03BB\u03AC\u03B4\u03BF\u03C2 \u03C4\u03C9\u03BD \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03CE\u03BD \u03C0\u03BF\u03C5 \u03B1\u03C3\u03C7\u03BF\u03BB\u03B5\u03AF\u03C4\u03B1\u03B9 \u03BC\u03B5 \u03C4\u03B7 \u03BC\u03B5\u03BB\u03AD\u03C4\u03B7 \u03C4\u03C9\u03BD \u03C0\u03B5\u03C0\u03B5\u03C1\u03B1\u03C3\u03BC\u03AD\u03BD\u03C9\u03BD \u03BA\u03B1\u03B9 \u03C4\u03C9\u03BD \u03AC\u03C0\u03B5\u03B9\u03C1\u03C9\u03BD \u03B1\u03BB\u03BB\u03AC \u03BC\u03B5\u03C4\u03C1\u03AE\u03C3\u03B9\u03BC\u03C9\u03BD \u03B4\u03B9\u03B1\u03BA\u03C1\u03B9\u03C4\u03CE\u03BD . \u03A0\u03C4\u03C5\u03C7\u03AD\u03C2 \u03BC\u03B5 \u03C4\u03B9\u03C2 \u03BF\u03C0\u03BF\u03AF\u03B5\u03C2 \u03B1\u03C3\u03C7\u03BF\u03BB\u03B5\u03AF\u03C4\u03B1\u03B9 \u03B7 \u03C3\u03C5\u03BD\u03B4\u03C5\u03B1\u03C3\u03C4\u03B9\u03BA\u03AE 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\u03C4\u03B1 \u03BA\u03C1\u03B9\u03C4\u03AE\u03C1\u03B9\u03B1(\u03CC\u03C0\u03C9\u03C2 \u03C4\u03B1 \u03BA\u03B1\u03B9 \u03C4\u03B7\u03BD ) \u03C4\u03B7\u03BD \u03B5\u03CD\u03C1\u03B5\u03C3\u03B7 \"\u03BC\u03B5\u03B3\u03B1\u03BB\u03CD\u03C4\u03B5\u03C1\u03BF\u03C5\", \"\u03BC\u03B9\u03BA\u03C1\u03CC\u03C4\u03B5\u03C1\u03BF\u03C5\" \u03AE \"\u03B2\u03AD\u03BB\u03C4\u03B9\u03C3\u03C4\u03BF\u03C5\" \u03B1\u03BD\u03C4\u03B9\u03BA\u03B5\u03B9\u03BC\u03AD\u03BD\u03BF\u03C5 ( \u03BA\u03B1\u03B9 ) \u03BA\u03B1\u03B9 \u03C4\u03B7\u03BD \u03BC\u03B5\u03BB\u03AD\u03C4\u03B7 \u03C3\u03C5\u03BD\u03B4\u03C5\u03B1\u03C3\u03C4\u03B9\u03BA\u03CE\u03BD \u03B4\u03BF\u03BC\u03CE\u03BD \u03C0\u03BF\u03C5 \u03C0\u03C1\u03BF\u03BA\u03CD\u03C0\u03C4\u03BF\u03C5\u03BD \u03C3\u03B5 \u03AD\u03BD\u03B1 \u03B1\u03BB\u03B3\u03B5\u03B2\u03C1\u03B9\u03BA\u03CC \u03C0\u03BB\u03B1\u03AF\u03C3\u03B9\u03BF \u03AE \u03B5\u03C1\u03C6\u03B1\u03BC\u03CC\u03B6\u03BF\u03BD\u03C4\u03B1\u03C2 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		"\u7D44\u5408\u305B\u6570\u5B66\uFF08\u304F\u307F\u3042\u308F\u305B\u3059\u3046\u304C\u304F\u3001\u82F1\u8A9E: combinatorics\uFF09\u3042\u308B\u3044\u306F\u7D44\u5408\u305B\u8AD6\uFF08\u304F\u307F\u3042\u308F\u305B\u308D\u3093\uFF09\u3068\u306F\u3001\u7279\u5B9A\u306E\u6761\u4EF6\u3092\u6E80\u305F\u3059\uFF08\u666E\u901A\u306F\u6709\u9650\u306E\uFF09\u5BFE\u8C61\u304B\u3089\u306A\u308B\u96C6\u307E\u308A\u3092\u7814\u7A76\u3059\u308B\u6570\u5B66\u306E\u5206\u91CE\u3002\u96E2\u6563\u6570\u5B66\u306E\u4E2D\u6838\u306E\u4E00\u3064\u3068\u3055\u308C\u308B\u3002\u7279\u306B\u554F\u984C\u3068\u3055\u308C\u308B\u3053\u3068\u3068\u3057\u3066\u3001\u96C6\u5408\u306B\u5165\u3063\u3066\u3044\u308B\u5BFE\u8C61\u3092\u6570\u3048\u305F\u308A\uFF08\u6570\u3048\u4E0A\u3052\u7684\u7D44\u5408\u305B\u8AD6\uFF09\u3001\u3044\u3064\u6761\u4EF6\u304C\u6E80\u305F\u3055\u308C\u308B\u306E\u304B\u3092\u5224\u5B9A\u3057\u3001\u305D\u306E\u6761\u4EF6\u3092\u6E80\u305F\u3057\u3066\u3044\u308B\u5BFE\u8C61\u3092\u69CB\u6210\u3057\u305F\u308A\u89E3\u6790\u3057\u305F\u308A\uFF08\u7D44\u5408\u305B\u30C7\u30B6\u30A4\u30F3\u3084\u30DE\u30C8\u30ED\u30A4\u30C9\u7406\u8AD6\uFF09\u3001\u300C\u6700\u5927\u300D\u300C\u6700\u5C0F\u300D\u300C\u6700\u9069\u300D\u306A\u5BFE\u8C61\u3092\u307F\u3064\u3051\u305F\u308A\uFF08\u6975\u5024\u7D44\u5408\u305B\u8AD6\u3084\u7D44\u5408\u305B\u6700\u9069\u5316\uFF09\u3001\u305D\u308C\u3089\u306E\u5BFE\u8C61\u304C\u6301\u3061\u3046\u308B\u4EE3\u6570\u7684\u69CB\u9020\u3092\u307F\u3064\u3051\u305F\u308A\uFF08\u4EE3\u6570\u7684\u7D44\u5408\u305B\u8AD6\uFF09\u3059\u308B\u3053\u3068\u304C\u6319\u3052\u3089\u308C\u308B\u3002"@ja ,
		"\u041A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0301\u0440\u0438\u043A\u0430 \u2014 \u0440\u0430\u0437\u0434\u0435\u043B \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438, \u043F\u043E\u0441\u0432\u044F\u0449\u0451\u043D\u043D\u044B\u0439 \u0440\u0435\u0448\u0435\u043D\u0438\u044E \u0437\u0430\u0434\u0430\u0447, \u0441\u0432\u044F\u0437\u0430\u043D\u043D\u044B\u0445 \u0441 \u0432\u044B\u0431\u043E\u0440\u043E\u043C \u0438 \u0440\u0430\u0441\u043F\u043E\u043B\u043E\u0436\u0435\u043D\u0438\u0435\u043C \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u043E\u0432 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u043E\u0433\u043E (\u0447\u0430\u0449\u0435 \u0432\u0441\u0435\u0433\u043E \u043A\u043E\u043D\u0435\u0447\u043D\u043E\u0433\u043E) \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u0432 \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0438\u0438 \u0441 \u0437\u0430\u0434\u0430\u043D\u043D\u044B\u043C\u0438 \u043F\u0440\u0430\u0432\u0438\u043B\u0430\u043C\u0438. \u041A\u0430\u0436\u0434\u043E\u0435 \u0442\u0430\u043A\u043E\u0435 \u043F\u0440\u0430\u0432\u0438\u043B\u043E \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u044F\u0435\u0442 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u0443\u044E \u0432\u044B\u0431\u043E\u0440\u043A\u0443 \u0438\u0437 \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u043E\u0432 \u0438\u0441\u0445\u043E\u0434\u043D\u043E\u0433\u043E \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430, \u043A\u043E\u0442\u043E\u0440\u0430\u044F \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u043D\u043E\u0439 \u043A\u043E\u043D\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0435\u0439. \u041F\u0440\u043E\u0441\u0442\u0435\u0439\u0448\u0438\u043C\u0438 \u043F\u0440\u0438\u043C\u0435\u0440\u0430\u043C\u0438 \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u043D\u044B\u0445 \u043A\u043E\u043D\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0439 \u044F\u0432\u043B\u044F\u044E\u0442\u0441\u044F \u043F\u0435\u0440\u0435\u0441\u0442\u0430\u043D\u043E\u0432\u043A\u0438, \u0441\u043E\u0447\u0435\u0442\u0430\u043D\u0438\u044F \u0438 \u0440\u0430\u0437\u043C\u0435\u0449\u0435\u043D\u0438\u044F. \u0422\u0438\u043F\u0438\u0447\u043D\u044B\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u0438\u043A\u0438: \n* \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0438\u0442\u044C \u043A\u043E\u043B\u0438\u0447\u0435\u0441\u0442\u0432\u043E \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u043D\u044B\u0445 \u043A\u043E\u043D\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0439, \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044E\u0449\u0438\u0445 \u0437\u0430\u0434\u0430\u043D\u043D\u044B\u043C \u043F\u0440\u0430\u0432\u0438\u043B\u0430\u043C (\u0432 \u0447\u0430\u0441\u0442\u043D\u043E\u0441\u0442\u0438, \u0434\u043E\u043A\u0430\u0437\u0430\u0442\u044C \u0438\u043B\u0438 \u043E\u043F\u0440\u043E\u0432\u0435\u0440\u0433\u043D\u0443\u0442\u044C \u0438\u0445 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043E\u0432\u0430\u043D\u0438\u0435); \n* \u043D\u0430\u0439\u0442\u0438 \u043F\u0440\u0430\u043A\u0442\u0438\u0447\u0435\u0441\u043A\u0438 \u043F\u0440\u0438\u0433\u043E\u0434\u043D\u044B\u0439 \u0430\u043B\u0433\u043E\u0440\u0438\u0442\u043C \u0438\u0445 \u043F\u043E\u043B\u043D\u043E\u0433\u043E \u043F\u043E\u0441\u0442\u0440\u043E\u0435\u043D\u0438\u044F; \n* \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0438\u0442\u044C \u0441\u0432\u043E\u0439\u0441\u0442\u0432\u0430 \u0437\u0430\u0434\u0430\u043D\u043D\u043E\u0433\u043E \u043A\u043B\u0430\u0441\u0441\u0430 \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u043D\u044B\u0445 \u043A\u043E\u043D\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0439. \u041A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u0438\u043A\u0430 \u0442\u0435\u0441\u043D\u043E \u0441\u0432\u044F\u0437\u0430\u043D\u0430 \u0441\u043E \u043C\u043D\u043E\u0433\u0438\u043C\u0438 \u0434\u0440\u0443\u0433\u0438\u043C\u0438 \u043E\u0431\u043B\u0430\u0441\u0442\u044F\u043C\u0438 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438 \u2014 \u0430\u043B\u0433\u0435\u0431\u0440\u043E\u0439, \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0435\u0439, \u0442\u0435\u043E\u0440\u0438\u0435\u0439 \u0432\u0435\u0440\u043E\u044F\u0442\u043D\u043E\u0441\u0442\u0435\u0439, \u0442\u0435\u043E\u0440\u0438\u0435\u0439 \u0447\u0438\u0441\u0435\u043B \u0438 \u0434\u0440\u0443\u0433\u0438\u043C\u0438. \u041E\u043D\u0430 \u043F\u0440\u0438\u043C\u0435\u043D\u044F\u0435\u0442\u0441\u044F \u0432 \u0441\u0430\u043C\u044B\u0445 \u0440\u0430\u0437\u043B\u0438\u0447\u043D\u044B\u0445 \u043E\u0431\u043B\u0430\u0441\u0442\u044F\u0445 \u0437\u043D\u0430\u043D\u0438\u0439, \u043D\u0430\u043F\u0440\u0438\u043C\u0435\u0440, \u0432 \u0433\u0435\u043D\u0435\u0442\u0438\u043A\u0435, \u0438\u043D\u0444\u043E\u0440\u043C\u0430\u0442\u0438\u043A\u0435, \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043A\u0435, \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0439 \u0444\u0438\u0437\u0438\u043A\u0435, \u043B\u0438\u043D\u0433\u0432\u0438\u0441\u0442\u0438\u043A\u0435. \u0422\u0435\u0440\u043C\u0438\u043D \u00AB\u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u0438\u043A\u0430\u00BB \u0431\u044B\u043B \u0432\u0432\u0435\u0434\u0451\u043D \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u043E\u0431\u0438\u0445\u043E\u0434 \u0432 1666 \u0433\u043E\u0434\u0443 \u041B\u0435\u0439\u0431\u043D\u0438\u0446\u0435\u043C \u0432 \u0442\u0440\u0443\u0434\u0435 \u00AB\u0420\u0430\u0441\u0441\u0443\u0436\u0434\u0435\u043D\u0438\u044F \u043E \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u043D\u043E\u043C \u0438\u0441\u043A\u0443\u0441\u0441\u0442\u0432\u0435\u00BB."@ru ,
		"\u041A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0301\u0440\u0438\u043A\u0430 (\u041A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u043D\u0438\u0439 \u0430\u043D\u0430\u043B\u0456\u0437) \u2014 \u0440\u043E\u0437\u0434\u0456\u043B \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438, \u043F\u0440\u0438\u0441\u0432\u044F\u0447\u0435\u043D\u0438\u0439 \u0440\u043E\u0437\u0432'\u044F\u0437\u0430\u043D\u043D\u044E \u0437\u0430\u0434\u0430\u0447 \u0432\u0438\u0431\u043E\u0440\u0443 \u0442\u0430 \u0440\u043E\u0437\u0442\u0430\u0448\u0443\u0432\u0430\u043D\u043D\u044F \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0456\u0432 \u0434\u0435\u044F\u043A\u043E\u0457, \u0437\u0430\u0437\u0432\u0438\u0447\u0430\u0439, \u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u043E\u0457 \u043C\u043D\u043E\u0436\u0438\u043D\u0438 \u0432\u0456\u0434\u043F\u043E\u0432\u0456\u0434\u043D\u043E \u0434\u043E \u0437\u0430\u0434\u0430\u043D\u0438\u0445 \u043F\u0440\u0430\u0432\u0438\u043B. \u041A\u043E\u0436\u043D\u0435 \u0442\u0430\u043A\u0435 \u043F\u0440\u0430\u0432\u0438\u043B\u043E \u0432\u0438\u0437\u043D\u0430\u0447\u0430\u0454 \u0441\u043F\u043E\u0441\u0456\u0431 \u043F\u043E\u0431\u0443\u0434\u043E\u0432\u0438 \u0434\u0435\u044F\u043A\u043E\u0457 \u043A\u043E\u043D\u0441\u0442\u0440\u0443\u043A\u0446\u0456\u0457 \u0456\u0437 \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0456\u0432 \u0432\u0438\u0445\u0456\u0434\u043D\u043E\u0457 \u043C\u043D\u043E\u0436\u0438\u043D\u0438, \u0449\u043E \u0437\u0432\u0435\u0442\u044C\u0441\u044F \u043A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u043D\u043E\u044E \u043A\u043E\u043D\u0444\u0456\u0433\u0443\u0440\u0430\u0446\u0456\u0454\u044E. \u0422\u043E\u043C\u0443 \u043D\u0430 \u043C\u0435\u0442\u0456 \u043A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u043D\u043E\u0433\u043E \u0430\u043D\u0430\u043B\u0456\u0437\u0443 \u0441\u0442\u043E\u0457\u0442\u044C \u0434\u043E\u0441\u043B\u0456\u0434\u0436\u0435\u043D\u043D\u044F \u043A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u043D\u0438\u0445 \u043A\u043E\u043D\u0444\u0456\u0433\u0443\u0440\u0430\u0446\u0456\u0439, \u0430\u043B\u0433\u043E\u0440\u0438\u0442\u043C\u0456\u0432 \u0457\u0445 \u043F\u043E\u0431\u0443\u0434\u043E\u0432\u0438, \u043E\u043F\u0442\u0438\u043C\u0456\u0437\u0430\u0446\u0456\u044F \u0442\u0430\u043A\u0438\u0445 \u0430\u043B\u0433\u043E\u0440\u0438\u0442\u043C\u0456\u0432, \u0430 \u0442\u0430\u043A\u043E\u0436 \u0440\u043E\u0437\u0432'\u044F\u0437\u0430\u043D\u043D\u044F \u0437\u0430\u0434\u0430\u0447 \u043F\u0435\u0440\u0435\u043B\u0456\u043A\u0443. \u041D\u0430\u0439\u043F\u0440\u043E\u0441\u0442\u0456\u0448\u0438\u043C\u0438 \u043F\u0440\u0438\u043A\u043B\u0430\u0434\u0430\u043C\u0438 \u043A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u043D\u0438\u0445 \u043A\u043E\u043D\u0444\u0456\u0433\u0443\u0440\u0430\u0446\u0456\u0439 \u0454 \u043F\u0435\u0440\u0435\u0441\u0442\u0430\u043D\u043E\u0432\u043A\u0438, \u0440\u043E\u0437\u043C\u0456\u0449\u0435\u043D\u043D\u044F, \u043A\u043E\u043C\u0431\u0456\u043D\u0430\u0446\u0456\u044F \u0442\u0430 \u0440\u043E\u0437\u0431\u0438\u0442\u0442\u044F. \u041A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u0438\u043A\u0430 \u043F\u043E\u0432'\u044F\u0437\u0430\u043D\u0430 \u0437 \u0431\u0430\u0433\u0430\u0442\u044C\u043C\u0430 \u0456\u043D\u0448\u0438\u043C\u0438 \u0440\u043E\u0437\u0434\u0456\u043B\u0430\u043C\u0438 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438. \u0422\u0435\u0440\u043C\u0456\u043D \u00AB\u043A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u0438\u043A\u0430\u00BB \u0432\u0432\u0456\u0432 \u041B\u044F\u0439\u0431\u043D\u0456\u0446, \u044F\u043A\u0438\u0439 \u0443 1666 \u0440\u043E\u0446\u0456 \u043E\u043F\u0443\u0431\u043B\u0456\u043A\u0443\u0432\u0430\u0432 \u0441\u0432\u043E\u044E \u043F\u0440\u0430\u0446\u044E \u00AB\u041C\u0456\u0440\u043A\u0443\u0432\u0430\u043D\u043D\u044F \u043F\u0440\u043E \u043A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u043D\u0435 \u043C\u0438\u0441\u0442\u0435\u0446\u0442\u0432\u043E\u00BB. \u0406\u043D\u043E\u0434\u0456 \u043F\u0456\u0434 \u043A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u0438\u043A\u043E\u044E \u0440\u043E\u0437\u0443\u043C\u0456\u044E\u0442\u044C \u0448\u0438\u0440\u0448\u0438\u0439 \u0440\u043E\u0437\u0434\u0456\u043B \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u043E\u0457 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438, \u0449\u043E \u0432\u043A\u043B\u044E\u0447\u0430\u0454 \u0442\u0435\u043E\u0440\u0456\u044E \u0433\u0440\u0430\u0444\u0456\u0432."@uk ,
		"Kombinatorika (kombinatorick\u00E1 matematika) je \u010D\u00E1st matematiky zab\u00FDvaj\u00EDc\u00ED se kolekcemi prvk\u016F mno\u017Ein s definovanou vnit\u0159n\u00ED strukturou. Ot\u00E1zky, kter\u00E9 kombinatorika \u0159e\u0161\u00ED, se obvykle t\u00FDkaj\u00ED po\u010Dtu n\u011Bjak\u00FDch objekt\u016F (nebo skupin objekt\u016F) s definovanou strukturou, speci\u00E1ln\u011B (pokud po\u010Det m\u016F\u017Ee b\u00FDt nulov\u00FD) existenc\u00ED objektu s definovanou strukturou."@cs ,
		"Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ad hoc solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is graph theory, which by itself has numerous natural connections to other areas. Combinatorics is used frequently in computer science to obtain formulas and estimates in the analysis of algorithms. A mathematician who studies combinatorics is called a combinatorialist."@en ,
		"Con il termine combinatoria o combinatorica (che comprende anche la geometria combinatoria) si intende il settore della matematica che studia insiemi finiti di oggetti semplici (interi, stringhe, nodi e collegamenti, punti e linee, configurazioni discrete, insiemi finiti, ...) che soddisfano propriet\u00E0 ben definite e tendenzialmente semplici."@it ,
		"Kombinatorik \u00E4r den gren av matematiken som studerar kombinationer, permutationer och uppr\u00E4kningar av element i m\u00E4ngder och de relationer som karakteriserar dessas egenskaper. Metoderna f\u00F6r detta \u00E4r grundl\u00E4ggande i den diskreta matematiken. F\u00F6reg\u00E5ngsm\u00E4n inom omr\u00E5det \u00E4r bland andra Blaise Pascal, Pierre de Fermat, Pierre R\u00E9mond de Montmort, James Stirling och br\u00F6derna Jacob och Johann Bernoulli. Ett enkelt exempel p\u00E5 ett kombinatoriskt problem \u00E4r fr\u00E5gan, om hur m\u00E5nga olika ordningsf\u00F6ljder det finns av en 52-korts kortlek. L\u00F6sningsmetoden \u00E4r k\u00E4nd sedan 2500 \u00E5r tillbaka och antalet f\u00F6ljder \u00E4r 52! (utl\u00E4ses \"fakulteten av 52\" eller \"52 fakultet\"), allts\u00E5 52\u00B751\u00B750\u00B7 \u00B7\u00B7\u00B7 \u00B73\u00B72\u00B71 vilket \u00E4r ungef\u00E4r lika med 8\u00B71067, eller en \u00E5tta f\u00F6ljd av 67 nollor."@sv ,
		"A combinat\u00F3ria \u00E9 um ramo da matem\u00E1tica que estuda cole\u00E7\u00F5es finitas de elementos que satisfazem crit\u00E9rios espec\u00EDficos determinados e se preocupa, em particular, com a \"contagem\" de elementos nessas cole\u00E7\u00F5es (combinat\u00F3ria enumerativa), com decidir se certo objeto \"\u00F3timo\" existe (combinat\u00F3ria extremal) e com estruturas \"alg\u00E9bricas\" que esses objetos possam ter (combinat\u00F3ria alg\u00E9brica). O assunto ganhou notoriedade ap\u00F3s a publica\u00E7\u00E3o de An\u00E1lise Combinat\u00F3ria por Percy Alexander MacMahon em 1915. Um dos destacados combinatorialistas foi Gian-Carlo Rota, que ajudou a formalizar o assunto a partir da d\u00E9cada de 1960. E, o engenhoso Paul Erd\u0151s trabalhou principalmente em problemas extremais. O estudo de como contar os objetos \u00E9 algumas vezes considerado separadamente como um campo da enumera\u00E7\u00E3o. Um exemplo de problema combinat\u00F3rio \u00E9 o seguinte: Quantas ordena\u00E7\u00F5es \u00E9 poss\u00EDvel fazer com um baralho de 52 cartas? O n\u00FAmero \u00E9 igual a 52! (ou seja, \"cinquenta e dois fatorial\"), que \u00E9 o produto de todos os n\u00FAmeros naturais de 1 at\u00E9 52. Pode parecer surpreendente o qu\u00E3o enorme \u00E9 esse n\u00FAmero, cerca de 8,065817517094 \u00D7 1067. Comparando este n\u00FAmero com alguns outros n\u00FAmeros grandes, ele \u00E9 maior que o quadrado do N\u00FAmero de Avogadro, 6,022 \u00D7 1023, quantidade equivalente a um mol\"."@pt ,
		"\uC870\uD569\uB860(\u7D44\u5408\u8AD6, \uC601\uC5B4: combinatorics) \uB610\uB294 \uC870\uD569\uC218\uD559(\u7D44\u5408\u6578\u5B78)\uC740 \uC720\uD55C\uD558\uAC70\uB098 \uAC00\uC0B0\uC801\uC778 \uAD6C\uC870\uB4E4\uC5D0 \uB300\uD558\uC5EC, \uC5B4\uB5A4 \uC8FC\uC5B4\uC9C4 \uC131\uC9C8\uC744 \uB9CC\uC871\uC2DC\uD0A4\uB294 \uAC83\uB4E4\uC758 \uAC00\uC9D3\uC218\uB098 \uC5B4\uB5A4 \uC8FC\uC5B4\uC9C4 \uC131\uC9C8\uC744 \uADF9\uB300\uD654\uD558\uB294 \uAC83\uC744 \uC5F0\uAD6C\uD558\uB294 \uC218\uD559 \uBD84\uC57C\uC774\uB2E4."@ko ,
		"Konbinatoria kontaketa-ebazkizunak aztertzen dituzten teknika matematikoen multzoa da. Zehatzago, konbinatoria multzo finituen kardinalen inguruko propietate eta ezaugarriak aztertzen arduratzen da, propietate berdinak dituzten elementuak zenbatu eta hauen arteko eraikuntzak ikasten dituelarik. Zenbaketa eta zerrendatze hutsaz arduratzen den arloari deritzo (adibidez, 10 pertsonako talde batean zenbat bikote ezberdin osa daitezke?); ezaugarri bati buruz multzoko elementu hobezina aurkitzeaz arduratzen den arloari, berriz, optimizazio edo deritzo (adibidez, 10 puntu harturik, puntu batetik bestera egiten diren ibilbide guztietatik zein da laburrena?). Konbinatoria aljebra abstraktuan, geometrian, grafo teorian eta probabilitateen kalkuluan erabiltzen da. Praktikan, informatikan eta ikerketa operatiboan aplikazio zuzenak ditu."@eu ,
		"La combinatoria es una rama de la matem\u00E1tica perteneciente al \u00E1rea de matem\u00E1ticas discretas que estudia la enumeraci\u00F3n, construcci\u00F3n y existencia de propiedades de configuraciones que satisfacen ciertas condiciones establecidas. Adem\u00E1s, estudia las ordenaciones o agrupaciones de un determinado n\u00FAmero de elementos. Los aspectos de la combinatoria incluyen contar las estructuras de un tipo y tama\u00F1o dado (combinatorias enumerativas), decidir cu\u00E1ndo pueden cumplirse ciertos criterios y construir y analizar objetos que cumplan los criterios (como en los dise\u00F1os combinatorios y la teor\u00EDa de matroides) encontrar objetos \"m\u00E1s grandes\", \"m\u00E1s peque\u00F1os\" u \"\u00F3ptimos\" (combinatoria extrema y optimizaci\u00F3n combinatoria), estudiar estructuras combinatorias surgidas en un contexto algebraico, o aplicar t\u00E9cnicas algebraicas a problemas combinatorios (combinatoria algebraica). Los problemas combinatorios surgen en muchas \u00E1reas de la matem\u00E1tica pura, especialmente en \u00E1lgebra, teor\u00EDa de probabilidades, topolog\u00EDa y geometr\u00EDa, y la combinatoria tambi\u00E9n tiene muchas aplicaciones en la optimizaci\u00F3n matem\u00E1tica, la inform\u00E1tica, la teor\u00EDa erg\u00F3dica y la f\u00EDsica estad\u00EDstica. Muchas cuestiones combinatoriales han sido hist\u00F3ricamente consideradas aisladamente, dando una soluci\u00F3n adecuada a un problema que surge en alg\u00FAn contexto matem\u00E1tico. A finales del siglo XX, sin embargo, se desarrollaron m\u00E9todos te\u00F3ricos poderosos y generales, convirtiendo la combinatoria en una rama independiente de las matem\u00E1ticas por derecho propio. Una de las partes m\u00E1s antiguas y accesibles de la combinatoria es la teor\u00EDa de grafos, que tambi\u00E9n tiene numerosas conexiones naturales a otras \u00E1reas. La combinatoria se utiliza con frecuencia en inform\u00E1tica para obtener f\u00F3rmulas y estimaciones en el an\u00E1lisis de algoritmos."@es ,
		"La combinat\u00F2ria \u00E9s una branca de les matem\u00E0tiques pures que s'ocupa de l'estudi d'objectes discrets (i normalment tamb\u00E9 finits). Una part de la combinat\u00F2ria inclou el \"comptar\" el nombre d'objectes que satisfan un criteri (combinat\u00F2ria enumerativa), decidir quan aquest criteri es compleix, i construir i analitzar els objectes que compleixen el criteri. Una de les \u00E0rees m\u00E9s antiga i m\u00E9s accessible de la combinat\u00F2ria \u00E9s la teoria de grafs. Hi ha molts patrons i teoremes relacionats amb l'estructura d'un conjunt combinatori. Aquests normalment se centren en la partici\u00F3 (combinaci\u00F3) o partici\u00F3 ordenada (permutaci\u00F3) d'un conjunt. Un exemple senzill \u00E9s saber quantes ordenacions es poden fer d'una baralla de 52 cartes. La resposta \u00E9s 52! (52 factorial), que aproximadament dona 8,0658\u00B71067."@ca ,
		"Kombinatoryka \u2013 dzia\u0142 matematyki, zajmuj\u0105cy si\u0119 badaniem struktur sko\u0144czonych lub niesko\u0144czonych, ale przeliczalnych. Np. okre\u015Blenie, ile jest podzbior\u00F3w k-elementowych w zbiorze n-elementowym stanowi jedno z typowych zagadnie\u0144 kombinatoryki. Nazwa dyscypliny pochodzi od G.W. Leibniza. Kombinatoryka sw\u00F3j rozw\u00F3j zawdzi\u0119cza rachunkowi prawdopodobie\u0144stwa, teorii graf\u00F3w, teorii informacji i innym dzia\u0142om matematyki stosowanej. Stanowi jeden z dzia\u0142\u00F3w matematyki dyskretnej. Kombinatoryka pos\u0142uguje si\u0119 terminologi\u0105 niewyst\u0119puj\u0105c\u0105 w innych dzia\u0142ach matematyki, st\u0105d pozorna jej odr\u0119bno\u015B\u0107. Najwa\u017Cniejszym jej zadaniem jest konstruowanie spe\u0142niaj\u0105cych pewne okre\u015Blone warunki odwzorowa\u0144 jednego zbioru sko\u0144czonego w drugi oraz znajdowanie wzor\u00F3w na liczb\u0119 tych odwzorowa\u0144."@pl ,
		"Kombinatoriko estas bran\u0109o de la matematiko, en kiu oni studas la ekziston kaj konstruon de diversaj kaj de elementoj la\u016D difinitaj reguloj, kaj ser\u0109as la nombrojn da kombinoj kaj aran\u011Doj de diversaj tipoj. Ekzemploj de tiaj kombinoj estas aran\u011Da\u0135oj, kombina\u0135oj permuta\u0135oj, kaj Latinaj kvadratoj. Apero de \u0109efaj nocioj kaj evoluo de kombinatora analizo okazis paralele kun aliaj bran\u0109oj de matematiko, tiaj kiaj estas algebro, nombroteorio, probabloteorio, kun kiuj \u011Di havas proksimajn rilatojn. Esti\u011Do de kombinatoriko, kiel matematika scienco, estas ligita kun la verkoj de Blaise Pascal kaj Pierre De Fermat. \u0108i tiuj verkoj, fari\u011Dintaj bazo por la teorio de probabloj, samtempe enhavis principojn por la determino de nombro de kombina\u0135oj por finia aro. La gravan rolon en la evoluo de kombinatoraj metodoj plenumis Gottfried Wilhelm Leibniz, Jakob Bernoulli kaj Leonhard Euler. De la 50-aj jaroj de la 20-a jarcento intereso pri kombinatoriko revivi\u011Das pro la impeta evoluo de komputiko, cibernetiko, diskreta matematiko, kaj informteorio. La \u0109efaj konceptoj de kombinatoriko estas: \n* Faktorialo - la produto 1\u00B72\u00B73\u00B7...\u00B7n; \u011Di estas signita per la simbolo n! La faktorialo de 5 estas:5!=1\u00B72\u00B73\u00B74\u00B75=120 \n* Permuta\u0135o - \u0108iu el la eblaj diversaj manieroj vicigi la elementojn de certa aro. La diversaj permuta\u0135oj de la elementoj a, b, c estas: abc, acb, bac, bca, cab, cba. La nombro de eblaj permuta\u0135oj de n elementoj estas \u0109iam n! . \n* Aran\u011Da\u0135o - \u0108iu el la diversaj manieroj fari ordigitan liston de k elementoj el aro de n elementoj (do, du aran\u011Doj estas samaj nur kondi\u0109e ke inter la du listoj ekzistu diferenco a\u016D pri la loko, a\u016D pri la identeco de almena\u016D unu elemento). La nombron de tiaj aran\u011Da\u0135oj esprimas la formulo \n* Kombina\u0135o ( a\u016D kombinacio) - de k el n elementoj. Aro de k elementoj, elektita el la aro da n elementoj: la eblaj kombinacioj de 2 el la 4 elementoj a, b, c, d estas: ab, ac, ad, bc, bd, cd. La K de k el n estas la nombro de la aran\u011Da\u0135oj dividita de la nombro de permuta\u0135oj en k: \n* Latina kvadrato - aran\u011Do de n simboloj en kvadrato kun n horizontalaj linioj kaj n vertikalaj linioj, tiel ke, \u0109iu simbolo aperas \u011Duste unu fojon en \u0109iu horizontala linio kaj \u011Duste unu fojon en \u0109iu vertikala linio."@eo ,
		"En math\u00E9matiques, la combinatoire, appel\u00E9e aussi analyse combinatoire, \u00E9tudie les configurations de collections finies d'objets ou les combinaisons d'ensembles finis, et les d\u00E9nombrements."@fr ,
		"\u0627\u0644\u062A\u0631\u0643\u064A\u0628\u0627\u062A \u0623\u0648 \u0627\u0644\u062A\u0648\u0627\u0641\u0642\u064A\u0627\u062A (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Combinatorics)\u200F \u0647\u064A \u0623\u062D\u062F \u0641\u0631\u0648\u0639 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0627\u0644\u062A\u064A \u062A\u062F\u0631\u0633 \u0627\u0644\u0628\u064F\u0646\u0649 \u0627\u0644\u0645\u062A\u0642\u0637\u0639\u0629 \u0627\u0644\u0645\u0646\u062A\u0647\u064A\u0629 \u0648\u0627\u0644\u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u0639\u062F. \u062A\u062A\u0636\u0645\u0646 \u0627\u0644\u062A\u0631\u0643\u064A\u0628\u0627\u062A \u0639\u062F\u0651 \u0627\u0644\u0639\u0646\u0627\u0635\u0631 \u0641\u064A \u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0627\u062A\u060C \u0645\u0639 \u062A\u062D\u062F\u064A\u062F \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062A \u062A\u062A\u0648\u0627\u0641\u0642 \u0645\u0639 \u0627\u0644\u0645\u0639\u0627\u064A\u064A\u0631 \u0627\u0644\u0645\u0637\u0644\u0648\u0628\u0629\u060C \u0648\u0643\u0630\u0644\u0643 \u062F\u0631\u0627\u0633\u0629 \u0628\u0646\u0627\u0621 \u0648\u062A\u062D\u0644\u064A\u0644 \u0627\u0644\u0643\u0627\u0626\u0646\u0627\u062A \u0627\u0644\u062A\u064A \u062A\u062D\u0642\u0642 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u064A\u064A\u0631 (\u0643\u0645\u0627 \u0641\u064A \u0648\u0646\u0638\u0631\u064A\u0629 )\u060C \u064A\u0647\u062A\u0645 \u0647\u0630\u0627 \u0627\u0644\u0639\u0644\u0645 \u0623\u064A\u0636\u0627\u064B \u0628\u0625\u064A\u062C\u0627\u062F \u0627\u0644\u0643\u0627\u0626\u0646\u0627\u062A \u0627\u0644\u0623\u0643\u0628\u0631 \u0623\u0648 \u0627\u0644\u0623\u0635\u063A\u0631 \u0623\u0648 \u0627\u0644\u0623\u0641\u0636\u0644 (\u0641\u064A\u0645\u0627 \u064A\u0639\u0631\u0641 \u0648\u0627\u0644\u062A\u0648\u0627\u0641\u0642\u064A\u0627\u062A \u0627\u0644\u062A\u062D\u0633\u064A\u0646\u064A\u0629). \u0648\u062F\u0631\u0627\u0633\u0629 \u0627\u0644\u0647\u064A\u0643\u0644 \u0627\u0644\u062A\u0631\u0643\u064A\u0628\u064A \u0627\u0644\u0638\u0627\u0647\u0631 \u0641\u064A \u0645\u062D\u062A\u0648\u0649 \u062C\u0628\u0631\u064A\u060C \u0623\u0648 \u062A\u0637\u0628\u064A\u0642 \u062A\u0642\u0646\u064A\u0627\u062A \u0627\u0644\u062C\u0628\u0631 \u0644\u062D\u0644 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u062A\u0631\u0643\u064A\u0628\u0627\u062A."@ar ,
		"Kombinatorika adalah cabang matematika yang membahas sifat-sifat dan cara menghitung struktur-struktur terhingga. Kombinatorika berkaitan erat dengan cabang-cabang matematika lain, dan memiliki banyak penerapan di ilmu logika sampai biologi evolusioner sampai ilmu komputer. Dalam matematika murni, permasalahan kombinatorika banyak ditemukan khususnya di aljabar, teori peluang, topologi, geometri, dan bidang-bidang terapannya. Tidak ada kesepakatan umum mengenai cakupan dari ilmu kombinatorika. Menurut , definisi ilmu ini sulit karena berurusan dengan sangat banyak [sub]cabang matematika. Cakupan kombinatorika dapat dideskripsikan lewat tipe-tipe masalah yang dikerjakan: \n* Mencacah (enumerasi) banyaknya struktur atau susunan yang berkaitan dengan sistem hingga, \n* Menentukan keberadaan struktur yang memenuhi kriteria-kriteria yang diinginkan, \n* Membuat (mengonstruksi) struktur-struktur tersebut, mungkin dalam banyak cara, dan \n* Melakukan optimisasi untuk mendapatkan struktur atau solusi \"terbaik\" dari satu atau beberapa kriteria; sebagai contoh \"terbesar\" atau \"terkecil\". Walaupun berfokus pada sistem hingga, beberapa permasalahan dan teknik kombinatorika dapat diperumum ke bentuk tak hingga (yang diskret dan terhitung). Banyak permasalahan kombinatorika pada awalnya muncul secara terisolasi, mengakibatkan banyak solusi-solusi ad hoc (spesifik) tergantung konteks pembahasan. Tapi pada akhir abad ke-20, konsep teoritis kombinatorika dikembangkan dan membuat kombinatorika menjadi cabang matematika terpisah."@in ,
		"Combinatoriek of combinatieleer is een tak van de wiskunde. In de combinatoriek bestudeert men eindige verzamelingen van objecten die aan gespecificeerde eigenschappen voldoen. In het bijzonder houdt men zich bezig met het \"tellen\" van objecten in deze verzamelingen en het bepalen of er zekere \"optimale\" objecten in een verzameling aanwezig zijn. Aangezien combinatoriek vooral over tellen gaat, wordt het wel de \"kunst van het tellen\" genoemd."@nl ,
		"Die Kombinatorik ist eine Teildisziplin der Mathematik, die sich mit endlichen oder abz\u00E4hlbar unendlichen diskreten Strukturen besch\u00E4ftigt und deshalb auch dem Oberbegriff diskrete Mathematik zugerechnet wird. Beispiele sind Graphen (Graphentheorie), teilgeordnete Mengen wie Verb\u00E4nde, Matroide, kombinatorische Designs, lateinische Quadrate, Parkettierungen, Permutationen von Objekten, Partitionen. Die Abgrenzung zu anderen Teilgebieten der diskreten Mathematik ist flie\u00DFend. Eine Definition von George P\u00F3lya bezeichnet die Kombinatorik als Untersuchung des Abz\u00E4hlens, der Existenz und Konstruktion von Konfigurationen. Je nach den verwendeten Methoden und Gegenst\u00E4nden unterscheidet man auch Teildisziplinen wie algebraische Kombinatorik, analytische Kombinatorik, geometrische und topologische Kombinatorik, probabilistische Kombinatorik, Kombinatorische Spieltheorie, Ramseytheorie. Speziell mit der Optimierung diskreter Strukturen besch\u00E4ftigt sich die kombinatorische Optimierung."@de ;
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dbr:Combinatorial_modelling	dbo:wikiPageWikiLink	dbr:Combinatorics .
dbr:Combinatoric	dbo:wikiPageWikiLink	dbr:Combinatorics ;
	dbo:wikiPageRedirects	dbr:Combinatorics .  <script>parent.window.postMessage('ixistenz.url:http://dbpedia.org/data/Combinatorics.n3', '*'); </script> <div id='browserdiffcontainer' style='position: fixed; right: 10px; top: 10vh; min-width: 60px;  border: 1px solid white; background: rgb(251, 189, 0);; opacity: 0.9; font-family: helvetica, arial, sans serif;  font-size: 12px; z-index: 20001; padding-bottom: 20px;'><div onclick="toggle('browserdiffcontainerlist'); return false;" style='background: rgb(151, 89, 0);; color: white; '><strong>&nbsp; <span class='glyphicon glyphicon-minus'></span> NODES</strong></div><div id='browserdiffcontainerlist' style='padding-left: 10px; padding-right: 5px; max-height: 50vh; overflow: auto; '><div><a href='#diffid883' style='color: white;' onClick="parent.window.postMessage('ixistenz.opendiff:883', '*');; return false;" style='text-decoration: none; '>Association </a> <a style='color: white;' href='#diffid883'><sup>1</sup></a></div><div><a href='#diffid884' style='color: white;' onClick="parent.window.postMessage('ixistenz.opendiff:884', '*');; return false;" style='text-decoration: none; '>Idea </a> <a style='color: white;' href='#diffid884'><sup>1</sup></a></div><div><a href='#diffid119' style='color: white;' onClick="parent.window.postMessage('ixistenz.opendiff:119', '*');; return false;" style='text-decoration: none; '>idea </a> <a style='color: white;' href='#diffid119'><sup>1</sup></a></div><div><a href='#diffid123' style='color: white;' onClick="parent.window.postMessage('ixistenz.opendiff:123', '*');; return false;" style='text-decoration: none; '>INTERN </a> <a style='color: white;' href='#diffid123'><sup>2</sup></a></div><div><a href='#diffid878' style='color: white;' onClick="parent.window.postMessage('ixistenz.opendiff:878', '*');; return false;" style='text-decoration: none; '>Note </a> <a style='color: white;' href='#diffid878'><sup>1</sup></a></div><div><a href='#diffid115' style='color: white;' onClick="parent.window.postMessage('ixistenz.opendiff:115', '*');; return false;" style='text-decoration: none; '>Project </a> <a style='color: white;' href='#diffid115'><sup>2</sup></a></div><div><a href='#diffid122' style='color: white;' onClick="parent.window.postMessage('ixistenz.opendiff:122', '*');; return false;" style='text-decoration: none; '>todo </a> <a style='color: white;' href='#diffid122'><sup>4</sup></a></div></div></div>
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