A Small Maximal Sidon Set In $Z_2^n$

Maximus Redman; Lauren Rose; Raphael Walker

A Small Maximal Sidon Set In $Z_2^n$

Combinatorics 2022-04-12 v3

Authors: Maximus Redman , Lauren Rose , Raphael Walker

Abstract

A Sidon set is a subset of an Abelian group with the property that each sum of two distinct elements is distinct. We construct a small maximal Sidon set of size $O((n \cdot 2^n)^{1/3})$ in the group $\mathbb{Z}_2^n$ , generalizing a result of Ruzsa concerning maximal Sidon sets in the integers.

Keywords

additive combinatorics combinatorial group theory set theory and dimension theory

Cite

@article{arxiv.2109.00292,
  title  = {A Small Maximal Sidon Set In $Z_2^n$},
  author = {Maximus Redman and Lauren Rose and Raphael Walker},
  journal= {arXiv preprint arXiv:2109.00292},
  year   = {2022}
}

Comments

7 pages, no figures. Final version to appear in SIDMA

A Small Maximal Sidon Set In $Z_2^n$

Abstract

Keywords

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