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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Permutation groups in Euclidean Ramsey theory


Author: Igor Kříž
Journal: Proc. Amer. Math. Soc. 112 (1991), 899-907
MSC: Primary 05D10; Secondary 20B25
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1065087-9
PII: S 0002-9939(1991)1065087-9
Article copyright: © Copyright 1991 American Mathematical Society



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