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.
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. . Available at: https://scholarship.claremont.edu/jhm/vol16/iss2/3
