R. I. Prosanov, “Upper Bounds for the Chromatic Numbers of Euclidean Spaces with Forbidden Ramsey Sets”, Mat. Zametki, 103:2 (2018), 248–257; Math. Notes, 103:2 (2018), 243

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Matematicheskie Zametki, 2018, Volume 103, Issue 2, Pages 248–257
DOI: https://doi.org/10.4213/mzm11397 (Mi mzm11397)

This article is cited in 16 scientific papers (total in 16 papers)

Upper Bounds for the Chromatic Numbers of Euclidean Spaces with Forbidden Ramsey Sets

R. I. Prosanov

Lomonosov Moscow State University

Full-text PDF (493 kB) Citations (16)

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DOI: https://doi.org/10.4213/mzm11397

Abstract: The chromatic number of a Euclidean space $\mathbb R^n$ with a forbidden finite set $C$ of points is the least number of colors required to color the points of this space so that no monochromatic set is congruent to $C$. New upper bounds for this quantity are found.

Keywords: Euclidean Ramsey theory, chromatic number of space.

Received: 01.10.2016
Revised: 07.02.2017

English version:
Mathematical Notes, 2018, Volume 103, Issue 2, Pages 243–250
DOI: https://doi.org/10.1134/S000143461801025X

Bibliographic databases:

Document Type: Article

UDC: 514.17

Language: Russian

Citation: R. I. Prosanov, “Upper Bounds for the Chromatic Numbers of Euclidean Spaces with Forbidden Ramsey Sets”, Mat. Zametki, 103:2 (2018), 248–257; Math. Notes, 103:2 (2018), 243–250

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Linking options:

https://www.mathnet.ru/eng/mzm11397

https://doi.org/10.4213/mzm11397

https://www.mathnet.ru/eng/mzm/v103/i2/p248

This publication is cited in the following 16 articles:

Nóra Frankl, Andrey Kupavskii, Arsenii Sagdeev, “Max-norm Ramsey theory”, European Journal of Combinatorics, 118 (2024), 103918
V. Kirova, A. Sagdeev, “Two-colorings of normed spaces without long monochromatic unit arithmetic progressions”, SIAM J. Discrete Math., 37:2 (2023), 718
A. B. Kupavskii, A. A. Sagdeev, N. Frankl, “Infinite sets can be Ramsey in the Chebyshev metric”, Russian Math. Surveys, 77:3 (2022), 549–551
V. O. Kirova, A. A. Sagdeev, “Two-colorings of normed spaces with no long monochromatic unit arithmetic progressions”, Dokl. Math., 106:2 (2022), 348–350
A. Kupavskii, A. Sagdeev, “All finite sets are Ramsey in the maximum norm”, Forum Math. Sigma, 9 (2021), e55
Nóra Frankl, Andrey Kupavskii, Arsenii Sagdeev, Trends in Mathematics, 14, Extended Abstracts EuroComb 2021, 2021, 477
R. Prosanov, “A new proof of the larman-rogers upper bound for the chromatic number of the euclidean space”, Discret Appl. Math., 276:SI (2020), 115–120
A. A. Sagdeev, “On the Chromatic Numbers Corresponding to Exponentially Ramsey Sets”, J Math Sci, 247:3 (2020), 488
L. I. Bogolubsky, A. M. Raigorodskii, “A Remark on Lower Bounds for the Chromatic Numbers of Spaces of Small Dimension with Metrics $\ell_1$ and $\ell_2$”, Math. Notes, 105:2 (2019), 180–203
A. A. Sagdeev, “On a Frankl–Wilson Theorem”, Problems Inform. Transmission, 55:4 (2019), 376–395
A. A. Sagdeev, A. M. Raigorodskii, “On a Frankl-Wilson theorem and its geometric corollaries”, Acta Math. Univ. Comen., 88:3 (2019), 1029–1033
A. A. Sagdeev, “Improved Frankl–Rödl theorem and some of its geometric consequences”, Problems Inform. Transmission, 54:2 (2018), 139–164
A. Sagdeev, “On the Frankl–Rödl theorem”, Izv. Math., 82:6 (2018), 1196–1224
A. A. Sagdeev, “Exponentially Ramsey sets”, Problems Inform. Transmission, 54:4 (2018), 372–396
A. A. Sagdeev, “O khromaticheskikh chislakh, sootvetstvuyuschikh eksponentsialno ramseevskim mnozhestvam”, Kombinatorika i teoriya grafov. X, Zap. nauchn. sem. POMI, 475, POMI, SPb., 2018, 174–189
Roman Prosanov, “Chromatic numbers of spheres”, Discrete Mathematics, 341:11 (2018), 3123

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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