A Small Maximal Sidon Set In $Z_2^n$

TL;DR

This paper constructs a small maximal Sidon set in the group ^n, extending previous results from integers to vector spaces over , with implications for additive combinatorics.

Contribution

It introduces a new construction of small maximal Sidon sets in ^n, generalizing Ruzsa's work from integers to vector spaces.

Findings

Constructed a maximal Sidon set of size O((n ^n)^{1/3}) in ^n

Extended Ruzsa's results from integers to ^n

Provided bounds on the size of maximal Sidon sets in ^n

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.