On rainbow isosceles 𝑛-simplexes-Reference-Cited by-同舟云学术

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On rainbow isosceles 𝑛-simplexes

Published:2022-03-17 Issue:4 Volume:29 Page:543-549
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Kharazishvili Alexander¹

Affiliation:

1. A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University , 6 Tamarashvili Str.,0177, Georgia; and I. Vekua Institute of Applied Mathematics, I. Javakhishvili Tbilisi State University, 2, University Str. , Tbilisi 0186 , Georgia

Abstract

Abstract It is proved that, for certain types of ( n + 1 )

(n+1)

-colorings of the Euclidean space R n

\mathbf{R}^{n}

, there are continuum many “rainbow” isosceles 𝑛-simplexes in R n

\mathbf{R}^{n}

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2022-2147/pdf

Reference19 articles.

1. M. Aigner and G. M. Ziegler, Proofs from The Book, 3rd ed., Springer, Berlin, 2004.

2. D. Coulson, A 15-colouring of 3-space omitting distance one, Discrete Math. 256 (2002), no. 1–2, 83–90.

3. L. Danzer, B. Grünbaum and V. Klee, Helly’s theorem and its relatives, Proceedings of Symposia in Pure Mathematics. Vol. 7 American Mathematical Society, Providence (1963), 101–180.

4. A. D. N. J. de Grey, The chromatic number of the plane is at least 5, Geombinatorics 28 (2018), no. 1, 18–31.

5. R. Engelking, General Topology, PWN, Warszawa, 1985.

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