{
  "id": "1011.0580",
  "version": "v1",
  "published": "2010-11-02T11:42:15.000Z",
  "updated": "2010-11-02T11:42:15.000Z",
  "title": "Ramsey Theory for Words Representing Rationals",
  "authors": [
    "Vassiliki Farmaki",
    "Andreas Koutsogiannis"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Ramsey theory for words over a finite alphabet was unified in the work of Carlson and Furstenberg-Katznelson. Carlson, in the same work, outlined a method to extend the theory for words over an infinite alphabet, but subject to a fixed dominating principle, proving in particular an Ellentuck version, and a corresponding Ramsey theorem for k=1. In the present work we develop in a systematic way a Ramsey theory for words (in fact for {\\omega}-Z*-located words) over a doubly infinite alphabet extending Carlson's approach (to countable ordinals and Schreier-type families), and we apply this theory, exploiting the Budak-Isik-Pym representation, to obtain a partition theory for the set of rational numbers. Furthermore, we show that the theory can be used to obtain partition theorems for arbitrary semigroups, stronger than known ones.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-02T11:42:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ramsey theory",
      "words representing rationals",
      "infinite alphabet extending carlsons approach",
      "doubly infinite alphabet extending carlsons"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.0580F"
    }
  }
}