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Proceedings of the American Mathematical Society

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Permutation groups in Euclidean Ramsey theory


Author: Igor Kříž
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
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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.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1991-1065087-9
Article copyright: © Copyright 1991 American Mathematical Society

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