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Diskr. Mat., 2018, Volume 30, Issue 3, Pages 117–126 (Mi dm1502)  

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 $(A_1,…,A_k)$ of subsets of a group $G$ is called $k$-solution-free family if the equation $x_1+…+x_k=0$ has no solution in $(A_1,…,A_k)$ such that $x_1\in A_1,…,x_k\in A_k$. 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

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00593A


DOI: https://doi.org/10.4213/dm1502

Full text: PDF file (534 kB)
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English version:
Discrete Mathematics and Applications, 2019, 29:6, 401–407

Bibliographic databases:

UDC: 519.115
Received: 05.02.2018

Citation: A. A. Sapozhenko, V. G. Sargsyan, “Asymptotics for the logarithm of the number of $k$-solution-free sets in Abelian groups”, Diskr. Mat., 30:3 (2018), 117–126; Discrete Math. Appl., 29:6 (2019), 401–407

Citation in format AMSBIB
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\paper Asymptotics for the logarithm of the number of $k$-solution-free sets in Abelian groups
\jour Diskr. Mat.
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\vol 30
\issue 3
\pages 117--126
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\jour Discrete Math. Appl.
\yr 2019
\vol 29
\issue 6
\pages 401--407
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  • https://doi.org/10.4213/dm1502
  • http://mi.mathnet.ru/eng/dm/v30/i3/p117

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