How Many Cards Should You Lay Out in a Game of EvenQuads: A Detailed Study of Caps in AG(n,2)

We define a cap in the affine geometry AG ( n , 2 ) to be a subset in which any collection of 4 points is in general position. In this paper, we classify, up to affine equivalence, all caps in AG ( n , 2 ) of size k ≤ 9 . As a result, we obtain a complete characterization of caps in dimension n ≤ 6...

Full description

Saved in:
Bibliographic Details
Published inLa matematica Vol. 2; no. 2; pp. 382 - 419
Main Authors Crager, Julia, Flores, Felicia, Goldberg, Timothy E., Rose, Lauren L., Rose-Levine, Daniel, Thornburgh, Darrion, Walker, Raphael
Format Journal Article
LanguageEnglish
Published New York Springer US 2023
Subjects
Mathematics
Mathematics and Statistics
Original Research Article
Recreational mathematics
Finite geometry
Affine geometry
51E10
Combinatorics
Sidon sets
05B25
Caps
51E15
Online AccessGet full text

Cover

More Information
Summary:We define a cap in the affine geometry AG ( n , 2 ) to be a subset in which any collection of 4 points is in general position. In this paper, we classify, up to affine equivalence, all caps in AG ( n , 2 ) of size k ≤ 9 . As a result, we obtain a complete characterization of caps in dimension n ≤ 6 , in particular complete and maximal caps. Since the EvenQuads card deck is a model for AG ( 6 , 2 ) , as a consequence, we determine the probability that an arbitrary k -card layout contains a quad.
ISSN:2730-9657
DOI:10.1007/s44007-023-00047-0