{
  "id": "2105.07689",
  "version": "v2",
  "published": "2021-05-17T09:19:12.000Z",
  "updated": "2021-06-13T20:15:16.000Z",
  "title": "Simplices and Regular Polygonal Tori in Euclidean Ramsey Theory",
  "authors": [
    "Miltiadis Karamanlis"
  ],
  "comment": "7 pages; corrected typos",
  "categories": [
    "math.CO"
  ],
  "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 K\\v{r}\\'{i}\\v{z}'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 R\\\"{o}dl.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2021-06-13T20:15:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D10",
      "05C55",
      "52C99"
    ],
    "keywords": [
      "regular polygonal torus",
      "euclidean ramsey theory",
      "finite affinely independent set",
      "finite product",
      "regular polygons"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}