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

A 2-cap in the affine geometry \(AG(n, q)\) is a subset of 4 points in general position. In this paper we classify all 2-caps in \(AG(n, 2)\), up to affine equivalence, for \(n \leq 6\). We also provide structural results for general \(n\). Since the EvenQuads card deck is a model for \(AG(6, 2)\),...

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Bibliographic Details
Published inarXiv.org
Main Authors Crager, Julia, Flores, Felicia, Goldberg, Timothy E, Rose, Lauren L, Rose-Levine, Daniel, Thornburgh, Darrion, Walker, Raphael
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 10.12.2022
Subjects
Affine transformations
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Summary:A 2-cap in the affine geometry \(AG(n, q)\) is a subset of 4 points in general position. In this paper we classify all 2-caps in \(AG(n, 2)\), up to affine equivalence, for \(n \leq 6\). We also provide structural results for general \(n\). 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.
ISSN:2331-8422