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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 506, Pages 54–56
DOI: https://doi.org/10.31857/S2686954322050125 (Mi danma298) 		 
MATHEMATICS

Two-colorings of normed spaces with no long monochromatic unit arithmetic progressions

V. O. Kirovaa, A. A. Sagdeevb

a Lomonosov Moscow State University
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow oblast, Russia
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DOI: https://doi.org/10.31857/S2686954322050125
Abstract: Given 1 $\le p\le\infty$ and $n\in\mathbb N$, we construct a two-coloring of the $n$-dimensional space $\mathbb{R}_p^n$ equipped with the $l_p$ norm such that all sufficiently long unit arithmetic progressions contain points of both colors.
Keywords: coloring, chromatic number, unit arithmetic progression.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-775.2022.1.1
Russian Foundation for Basic Research 20-31-90009
Contest «Young Russian Mathematics»
This work was supported in part by the Program “Leading Scientific Schools” (grant no. NSh-775.2022.1.1) and by the Russian Foundation for Basic Research (project no. 20-31-90009). Sagdeev is a winner of the contest “Young Russian Mathematics” and is grateful to its sponsors and referees.
Presented: V. V. Kozlov
Received: 18.05.2022
Revised: 24.06.2022
Accepted: 16.07.2022
English version:
Doklady Mathematics, 2022, Volume 106, Issue 2, Pages 348–350
DOI: https://doi.org/10.1134/S1064562422050143
Bibliographic databases:
Document Type: Article
UDC: 519.1
Language: Russian
Citation: V. O. Kirova, A. A. Sagdeev, “Two-colorings of normed spaces with no long monochromatic unit arithmetic progressions”, Dokl. RAN. Math. Inf. Proc. Upr., 506 (2022), 54–56; Dokl. Math., 106:2 (2022), 348–350
Citation in format AMSBIB
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\by V.~O.~Kirova, A.~A.~Sagdeev
\paper Two-colorings of normed spaces with no long monochromatic unit arithmetic progressions
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 506
\pages 54--56
\mathnet{http://mi.mathnet.ru/danma298}
\crossref{https://doi.org/10.31857/S2686954322050125}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4531984}
\elib{https://elibrary.ru/item.asp?id=49787602}
\transl
\jour Dokl. Math.
\yr 2022
\vol 106
\issue 2
\pages 348--350
\crossref{https://doi.org/10.1134/S1064562422050143}
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