Geodesic
Asymptotics for the logarithm of~the~number of~$(k,l)$-solution-free collections in~an~interval of~naturals
Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 2, pp. 129-144.

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A collection $(A_1,\dots,A_{k+l})$ of subsets of an interval $[1,n]$ of naturals is called $(k,l)$-solution-free if there is no set $(a_1,\dots,$ $a_{k+l})\in A_1\times\dots\times A_{k+l}$ that is a solution to the equation $x_1+\dots+x_k=x_{k+1}+\dots+x_{k+l}$. We obtain the asymptotics for the logarithm of the number of sets $(k,l)$-free of solutions in an interval $[1,n]$ of naturals. Bibliogr. 17.
Keywords: set, coset, characteristic function
Mots-clés : group, progression. 
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A. A. Sapozhenko; V. G. Sargsyan. Asymptotics for the logarithm of~the~number of~$(k,l)$-solution-free collections in~an~interval of~naturals. Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 2, pp. 129-144. http://geodesic.mathdoc.fr/item/DA_2019_26_2_a6/

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