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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Permutation groups in Euclidean Ramsey theory
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by Igor Kříž PDF
Proc. Amer. Math. Soc. 112 (1991), 899-907 Request permission

Abstract:

A finite subset of a Euclidean space is called Ramsey if for each $k$ and each $k$-coloring of a sufficiently dimensional Euclidean space $E$ there is a monochromatic isometrical embedding from $F$ to $E$. We show that if $F$ has a transitive solvable group of isometries then it is Ramsey. In particular, regular polygons are Ramsey. We also show that regular polyhedra in ${{\mathbf {R}}^3}$ are Ramsey.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 112 (1991), 899-907
  • MSC: Primary 05D10; Secondary 20B25
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1065087-9
  • MathSciNet review: 1065087