
COMMENTS

Or, largest size of an ndimensional 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
It may only be a conjecture that the interpretation in terms of the SET game gives the same sequence for all n as the maximal cap problem.  N. J. A. Sloane, Oct 25 2014, following a conversation with James Abello.


LINKS

Table of n, a(n) for n=0..6.
James Abello (DIMACS Institute, Rutgers University), The majority rule and combinatorial geometry (via the symmetric group), preprint, 2004.
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. 3340.
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 threeterm arithmetic progression, arXiv:1605.09223 [math.CO], 2016.
Michael Follett, et al. Partitions of AG (4, 3) into Maximal Caps, Discrete Math., 337 (2014), 18. 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, 1013.
Guardians of SET, SET Home Page.
Pierre Jalinière, Le jeu Set, Images des Mathématiques, CNRS, 2013.
Miriam Melnick, The Joy of SET, May 2011.
B. Monjardet, Acyclic domains of linear orders: a survey, in "The Mathematics of Preference, Choice and Order: Essays in Honor of Peter Fishburn", edited by Steven Brams, William V. Gehrlein and Fred S. Roberts, Springer, 2009, pp. 139160.
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.
SET card game, Official web site.
Terence Tao, Bounds for the first few density HalesJewett numbers, and related quantities.
Wikipedia, Set (game)
M. Zabrocki, The Joy of SET, 2001.
