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Asymptotics for the Logarithm of the Number of (k, l)-Solution-Free Collections in an Interval of Naturals

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Abstract

A collection (A1, … ,Ak+l) of subsets of an interval [1, n] of naturals is called (k, l)-solution-free if there is no set (a1, … , ak+l) ∈ A1 × ⋯ × Ak+l that is a solution to the equation x1 + ⋯ + xk = xk+1 + ⋯ + xk+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.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Leninskie gory 1, Moscow, 119991, Russia

    A. A. Sapozhenko & V. G. Sargsyan

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  1. A. A. Sapozhenko
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  2. V. G. Sargsyan
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Correspondence to A. A. Sapozhenko or V. G. Sargsyan.

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Russian Text © The Author(s), 2019, published in Diskretnyi Analiz i Issledovanie Operatsii, 2019, Vol. 26, No. 2, pp. 129–144.

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Sapozhenko, A.A., Sargsyan, V.G. Asymptotics for the Logarithm of the Number of (k, l)-Solution-Free Collections in an Interval of Naturals. J. Appl. Ind. Math. 13, 317–326 (2019). https://doi.org/10.1134/S1990478919020133

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  • DOI: https://doi.org/10.1134/S1990478919020133

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