Abstract / Synopsis
More specifically, we revisit the problem of determining the maximum number of cards that can be dealt in the SET® card game without any matches, which is well known to be equivalent to the problem of determining the size of a maximal cap in the affine space AG(4,3). We present a new approach to the problem by using partial difference sets, a method that is equivalent to using strongly regular graphs with a regular automorphism group. The paper includes several possible avenues for future investigations on how partial difference sets might be used in related problems.
DOI
10.5642/jhummath.LJJN8905
Recommended Citation
John Polhill, "The SET Card Game and Partitions into Maximal Caps: A Partial Difference Sets Approach," Journal of Humanistic Mathematics, Volume 16 Issue 2 (July 2026), pages 4-19. DOI: 10.5642/jhummath.LJJN8905. Available at: https://scholarship.claremont.edu/jhm/vol16/iss2/3
