This article is cited in 3 papers

Asymptotics of the logarithm of the number of $(k,l)$-sum-free sets in an Abelian group

V. G. Sargsyan

M. V. Lomonosov Moscow State University

Abstract: A subset $A$ of elements of a group $G$ is $(k,l)$-sum-free if $A$ does not contains solutions of the equation $x_1 + \ldots + x_k=y_1 + \ldots + y_l$. We have obtained asymptotics of the logarithm of the number of $(k,l)$-sum-free sets in an Abelian group.

Keywords: sum-free set, characteristic function, group, progression, coset.

UDC: 519.115+519.113.8

Received: 20.03.2014

DOI: 10.4213/dm1307

 English version: Discrete Mathematics and Applications, 2015, 25:2, 93–99

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