Geodesic
Asymptotics for the logarithm of the number of $k$-solution-free sets in Abelian groups
Diskretnaya Matematika, Tome 30 (2018) no. 3, pp. 117-126

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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. 
@article{DM_2018_30_3_a9,
     author = {A. A. Sapozhenko and V. G. Sargsyan},
     title = {Asymptotics for the logarithm of the number of $k$-solution-free sets in {Abelian} groups},
     journal = {Diskretnaya Matematika},
     pages = {117--126},
     publisher = {mathdoc},
     volume = {30},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2018_30_3_a9/}
}
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A. A. Sapozhenko; V. G. Sargsyan. Asymptotics for the logarithm of the number of $k$-solution-free sets in Abelian groups. Diskretnaya Matematika, Tome 30 (2018) no. 3, pp. 117-126. http://geodesic.mathdoc.fr/item/DM_2018_30_3_a9/