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.References
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- Peter Frankl and Vojtěch Rödl, All triangles are Ramsey, Trans. Amer. Math. Soc. 297 (1986), no. 2, 777–779. MR 854099, DOI 10.1090/S0002-9947-1986-0854099-6 F. P. Ramsey, On a problem of formal logic, Proc. London Math. Soc. 30 (1930), 264-286.
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