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arXiv · 2105.07689

Simplices and Regular Polygonal Tori in Euclidean Ramsey Theory

Miltiadis Karamanlis
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Abstract

We show that any finite affinely independent set can be isometrically embedded into a regular polygonal torus, that is, a finite product of regular polygons. As a consequence, with a straightforward application of Kříž's theorem, we get an alternative proof of the fact that all finite affinely independent sets are Ramsey, a result which was originally proved by Frankl and Rödl.

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Miltiadis Karamanlis. 2022-07-08. Simplices and Regular Polygonal Tori in Euclidean Ramsey Theory. https://doi.org/10.37236/10944

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