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Matematicheskie Zametki, 2017, Volume 102, Issue 3, Pages 436–444
DOI: https://doi.org/10.4213/mzm11248 (Mi mzm11248) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Maximal Subsets Free of Arithmetic Progressions in Arbitrary Sets

A. S. Semchenkov

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
Full-text PDF (434 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm11248
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 $[1,\dots,n]$. The study continues the work of Komlós, Sulyok, and Szemerédi.
Keywords: additive combinatorics, combinatorial number theory.
Funding agency Grant number
Russian Science Foundation 14-11-00433
This work was supported by the Russian Science Foundation under grant 14-11-00433.
Received: 31.05.2016
Revised: 17.08.2016
English version:
Mathematical Notes, 2017, Volume 102, Issue 3, Pages 396–402
DOI: https://doi.org/10.1134/S0001434617090097
Bibliographic databases:
Document Type: Article
UDC: 510.22
Language: Russian
Citation: A. S. Semchenkov, “Maximal Subsets Free of Arithmetic Progressions in Arbitrary Sets”, Mat. Zametki, 102:3 (2017), 436–444; Math. Notes, 102:3 (2017), 396–402
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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