Abstract

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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