Asymptotics for the logarithm of the number of $k$-solution-free sets in Abelian groups

A. A. Sapozhenko, V. G. Sargsyan

Lomonosov Moscow State University

Abstract: A family $(A_1,\dots,A_k)$ of subsets of a group $G$ is called $k$-solution-free family if the equation $x_1+\dots+x_k=0$ has no solution in $(A_1,\dots,A_k)$ such that $x_1\in A_1,\dots,x_k\in A_k$. We find the asymptotic behavior for the logarithm of the number of $k$-solution-free families in Abelian groups.

Keywords: set, characteristic function, group, progression, coset.

UDC: 519.115

Received: 05.02.2018

DOI: 10.4213/dm1502

 English version: Discrete Mathematics and Applications, 2019, 29:6, 401–407

Bibliographic databases:

• 
• 
• 
•