OFFSET
0,2
COMMENTS
Or, largest size of an n-dimensional capset (i.e., a subset of (Z/3Z)^n that does not contain any lines {a, a+r, a+2r}). - Terence Tao, Feb 20 2009
Or, size of maximal cap in the affine geometry AG(n+1,3). - N. J. A. Sloane, Oct 25 2014
LINKS
Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, arXiv:1705.07444 [math.NT], May 2017.
Robert A. Bosch, ‘Set’less Collections of SET Cards, 2000.
Brink, D. V., 1997, The search for SET. [via WayBackMachine]
Benjamin Lent Davis and Diane Maclagan, The Card Game SET, The Mathematical Intelligencer, Vol. 25:3 (Summer 2003), pp. 33-40.
Ernest Davis, Review of Romera-Paredes et al., 14 Dec 2023 Nature paper about FunSearch, January 7, 2024
Yves Edel, Home page.
Jordan S. Ellenberg, Bounds for cap sets, Quomodocumque Blog, May 13 2016.
Jordan S. Ellenberg, Dion Gijswijt, On large subsets of F_q^n with no three-term arithmetic progression, arXiv:1605.09223 [math.CO], 2016.
Michael Follett, et al. Partitions of AG (4, 3) into Maximal Caps, Discrete Math., 337 (2014), 1-8. Preprint: arXiv:1302.4703 [math.CO].
Dion Gijswijt, The card game SET: a mathematical challenge, 2016.
Dion Gijswijt, The Beautiful Mathematics of the Card Game SET, STAtOR, Netherlands Society for Statistics and Operations Research (VVSOR, 2019) Vol. 20, No. 2, 10-13.
Guardians of SET, SET Home Page.
Pierre Jalinière, Le jeu Set, Images des Mathématiques, CNRS, 2013.
Miriam Melnick, The Joy of SET, May 2011.
J. Peebles, Cap Set Bounds and Matrix Multiplication, Senior Thesis, Harvey Mudd College, 2013.
Ivars Peterson, SET Math.
Aaron Potechin, Maximal caps in AG(6, 3), Designs, Codes and Cryptography, Volume 46, Number 3, March 2008.
Bernardino Romera-Paredes, Mohammadamin Barekatain, Alexander Novikov, et al. Mathematical discoveries from program search with large language models, Nature 625, 468-475 (2024).
SET card game, Official web site.
Wikipedia, Set (game)
M. Zabrocki, The Joy of SET, 2001.
FORMULA
a(n) <= A003142(n).
Asymptotically, a(n) = O(3^n/n) and a(n) > (2.21...)^n. - Terence Tao, Feb 20 2009
Asymptotically, a(n) = o(2.756^n). - David Radcliffe, May 30 2016
CROSSREFS
KEYWORD
nonn,hard,more,nice
AUTHOR
Hans Havermann, Jan 23 2004
EXTENSIONS
a(6) from Terence Tao, Feb 20 2009
Edited by N. J. A. Sloane, Feb 21 2009
Edited by Andrey Zabolotskiy, Mar 01 2024
STATUS
approved