A Small Maximal Sidon Set In \(Z_2^n\)

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.

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-04
Main Authors: Redman, Maximus, Rose, Lauren, Walker, Raphael
Format: Article
Language:English
Subjects:
Group theory
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422