Email this article Asymptotics for the Logarithm of the Number of (k, l)-Solution-Free Collections in an Interval of Naturals
- Authors: Sapozhenko A.A.1, Sargsyan V.G.1
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Affiliations:
- Lomonosov Moscow State University
- Issue: Vol 13, No 2 (2019)
- Pages: 317-326
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/213188
- DOI: https://doi.org/10.1134/S1990478919020133
- ID: 213188
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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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About the authors
A. A. Sapozhenko
Lomonosov Moscow State University
Author for correspondence.
Email: sapozhenko@mail.ru
Russian Federation, Leninskie gory 1, Moscow, 119991
V. G. Sargsyan
Lomonosov Moscow State University
Author for correspondence.
Email: vahe_sargsyan@ymail.com
Russian Federation, Leninskie gory 1, Moscow, 119991
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