A090245 Maximum numbers of cards that would have no SET in an n-attribute version of the SET card game.
1, 2, 4, 9, 20, 45, 112
Offset: 0
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.
- D. V. Brink, The search for SET, 1997. [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, Caps, 2010.
- Yves Edel, Sandy Ferret, Ivan Landjev, Leo Storme, The classification of the largest caps in AG(5,3), Journal of Combinatorial Theory A, 99 (2002), 95-110.
- Jordan S. Ellenberg, Bounds for cap sets, Quomodocumque Blog, May 13 2016.
- Jordan S. Ellenberg and 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 poster (see also the thesis itself), 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.
- Terence Tao, Bounds for the first few density Hales-Jewett numbers, and related quantities.
- Wikipedia, Set (card 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
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
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