How many cards should you lay out in a game of EvenQuads?: A detailed study of caps in AG(n,2)
Abstract
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.
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