Maximum Number of Quads

Nikhil Byrapuram; Hwiseo; Choi; Adam Ge; Selena Ge; Tanya Khovanova; Sylvia Zia Lee; Evin Liang; Rajarshi Mandal; Aika Oki; Daniel Wu; Michael Yang

Maximum Number of Quads

Combinatorics 2023-10-17 v1

Authors: Nikhil Byrapuram , Hwiseo , Choi , Adam Ge , Selena Ge , Tanya Khovanova , Sylvia Zia Lee , Evin Liang , Rajarshi Mandal , Aika Oki , Daniel Wu , Michael Yang

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Abstract

We study the maximum number of quads among $\ell$ cards from an EvenQuads deck of size $2^n$ . This corresponds to enumerating quadruples of integers in the range $[0,\ell-1]$ such that their bitwise XOR is zero. In this paper, we conjecture a formula that calculates the maximum number of quads among $\ell$ cards.

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@article{arxiv.2310.09695,
  title  = {Maximum Number of Quads},
  author = {Nikhil Byrapuram and Hwiseo and Choi and Adam Ge and Selena Ge and Tanya Khovanova and Sylvia Zia Lee and Evin Liang and Rajarshi Mandal and Aika Oki and Daniel Wu and Michael Yang},
  journal= {arXiv preprint arXiv:2310.09695},
  year   = {2023}
}

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13 pages. 2 tables

Maximum Number of Quads

Abstract

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