Asymptotics of the number of sum-free sets in groups of prime order
type: Item
instance of: scholarly article
title: Asymptotics of the number of sum-free sets in groups of prime order
zbMATH Open document ID: 1292.11047
DOI: 10.1134/S1064562409010232
published in: Doklady Mathematics
publication date: 2012-11-15T00:00:00Z
review text: From the text: ``Let \(S(G)\) denote the family of all sum-free sets in the group \(G\), and let \(Z_p\) be the group of residues of order \(p\). The number \(s(Z_p)\), where \(p\) is a prime number, was estimated by Lev and Schoen.'' The goal of this paper is to prove the asymptotics of \(s(Z_p)\), where \(Z_p\) is a group of prime order \(p\). Specifically, we show that there are constants \(c_i\) \((i= 1, 2)\) such that, for sufficiently large prime numbers of the form \(p\equiv i\pmod 3\), \[ | S(Z_p)|\sim c_i(p-1)2^{[(p+1)/3]}. \] The proof is based on results of \textit{B. Green} and \textit{I. Z. Ruzsa} [Isr. J. Math. 147, 157--188 (2005; Zbl 1158.11311)]. as well as \textit{J.-M. Deshouillers} and \textit{V. F. Lev} [Bull. Lond. Math. Soc. 40, No. 5, 863--875 (2008; Zbl 1200.11078)]. Some more theorems are proved of related interest.
reviewed by: Olaf Ninnemann
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 6106391
author: Alexander Sapozhenko
MaRDI profile type: Publication
cites work: Independent sets in regular graphs and sum-free subsets of finite groups
cites work: On the Number of Sum-Free Sets
cites work: THE CAMERON–ERDOS CONJECTURE
cites work: Sum-free sets in abelian groups
cites work: Large sum-free sets in \(\mathbb Z/p\mathbb Z\)
cites work: Cameron-Erdős modulo a prime
cites work: Sum-free sets in Abelian groups.
full work available at URL: s1064562409010232
OpenAlex ID: W2054527129
description: scientific article; zbMATH DE number 6106391