Journal of Applied and Industrial Mathematics

, Volume 13, Issue 2, pp 317–326 | Cite as

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

  • A. A. SapozhenkoEmail author
  • V. G. SargsyanEmail author


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.


set group coset characteristic function progression 


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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