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arXiv · 2305.03012

Quasirandom additive sets and Cayley hypergraphs

Davi Castro-Silva
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Abstract

We study the interplay between notions of quasirandomness for additive sets and for hypergraphs. In particular, we show a strong connection between the notions of Gowers uniformity in the additive setting and discrepancy-type measures of quasirandomness in the hypergraph setting. Exploiting this connection, we provide a long list of disparate quasirandom properties regarding both additive sets and Cayley-type hypergraphs constructed from such sets, and show that these properties are all equivalent (in the sense of Chung, Graham and Wilson) with polynomial bounds on their interdependences.

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Davi Castro-Silva. 2023-05-04. Quasirandom additive sets and Cayley hypergraphs. https://arxiv.org/abs/2305.03012

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