Maximal subsets free of arithmetic progressions in arbitrary sets
- Authors: Semchankau A.S.1
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Affiliations:
- Moscow Institute of Physics and Technology (State University)
- Issue: Vol 102, No 3-4 (2017)
- Pages: 396-402
- Section: Article
- URL: https://ogarev-online.ru/0001-4346/article/view/150115
- DOI: https://doi.org/10.1134/S0001434617090097
- ID: 150115
Cite item
Abstract
The problem of determining the maximum cardinality of a subset containing no arithmetic progressions of length k in a given set of size n is considered. It is proved that it is sufficient, in a certain sense, to consider the interval [1,..., n]. The study continues the work of Komlós, Sulyok, and Szemerédi.
About the authors
A. S. Semchankau
Moscow Institute of Physics and Technology (State University)
Author for correspondence.
Email: leshaxim@mail.ru
Russian Federation, Dolgoprudnyi, Moscow Oblast
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