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

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We define a cap in the affine geometry \(\textrm{AG}(n,2)\) 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 \(\textrm{AG}(n,2)\) of size \(k \le 9\). As a result, we obtain a complete characterization of caps in dimension \(n \le 6\), in particular complete and maximal caps. Since the EvenQuads card deck is a model for \(\textrm{AG}(6,2)\), as a consequence, we determine the probability that an arbitrary k-card layout contains a quad.

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Correspondence to Timothy E. Goldberg.

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Crager, J., Flores, F., Goldberg, T.E. et al. How Many Cards Should You Lay Out in a Game of EvenQuads: A Detailed Study of Caps in \(\textrm{AG}(n,2)\). La Matematica 2, 382–419 (2023).

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