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A090245 Maximum numbers of cards that would have no SET in an n-attribute version of the SET card game. 4
1, 2, 4, 9, 20, 45, 112 (list; graph; refs; listen; history; text; internal format)
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

Asymptotically, a(n) = O(3^n/n) and a(n) > (2.21...)^n. - Terence Tao, Feb 20 2009

Apparently equivalent to a problem studied by Abello - see reference.

REFERENCES

James Abello (DIMACS, Rutgers), The majority rule and combinatorial geometry (via the symmetric group), preprint, 2004.

Ben Davis and Diane Maclagan, The card game Set. The Mathematical Intelligencer, 25, No. 3, 2003, 33-40.

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. 139-160.

J. Peebles, Cap Set Bounds and Matrix Multiplication, Senior Thesis, Harvey Mudd College, 2013; http://www.math.hmc.edu/seniorthesis/archives/2013/jpeebles/jpeebles-2013-thesis-poster.pdf

Aaron Potechin: Maximal caps in AG(6, 3), Designs, Codes and Cryptography, Volume 46, Number 3 / March, 2008

LINKS

Table of n, a(n) for n=0..6.

Brink, D. V., 1997, The search for SET

B. L. Davis and D. Maclagan, The Card Game SET

B. Davis and D. Maclagan, The Card Game SET, The Mathematical Intelligencer, Vol. 25:3 (Summer 2003), pp. 33-40.

Yves Edel, Home page

Guardians of SET, SET Home Page

Pierre Jalinière, Le jeu Set, Images des Mathématiques, CNRS, 2013.

Ivars Peterson, SET Math

Ivars Peterson, SET Math

Ivars Peterson, SET Math.

SET card game, Official web site

Terence Tao, Bounds for the first few density Hales-Jewett numbers, and related quantities

Zabrocki, M., 2001, The Joy of SET

FORMULA

a(n) <= A003142(n).

CROSSREFS

Cf. A090246, A156989.

Sequence in context: A188460 A111099 A000632 * A006958 A036617 A007902

Adjacent sequences:  A090242 A090243 A090244 * A090246 A090247 A090248

KEYWORD

hard,more,nonn,nice

AUTHOR

Hans Havermann, Jan 23 2004

EXTENSIONS

a(6) sent by Terence Tao, Feb 20 2009

Edited by N. J. A. Sloane, Feb 21 2009

STATUS

approved

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Last modified August 21 20:04 EDT 2014. Contains 245875 sequences.