{
  "id": "1106.4735",
  "version": "v4",
  "published": "2011-06-23T14:18:44.000Z",
  "updated": "2018-07-16T16:52:46.000Z",
  "title": "Hindman's Theorem, Ellis's Lemma, and Thompson's group $F$",
  "authors": [
    "Justin Tatch Moore"
  ],
  "comment": "This paper has now appeared but is largely obsolete: Conjectures 1.3 and 1.4 have since been refuted by the author. arXiv admin note: text overlap with arXiv:1209.2063",
  "journal": "Zbornik Radova. (Beograd), Selected topics in combinatorial analysis, 17(25):171-187, 2015",
  "categories": [
    "math.CO",
    "math.DS",
    "math.FA",
    "math.GN",
    "math.GR",
    "math.LO"
  ],
  "abstract": "The purpose of this article is to formulate conjectural generalizations of Hindman's Theorem and Ellis's Lemma for nonassociative binary systems and relate them to the amenability problem for Thompson's group $F$. Partial results are obtained for both conjectures. The paper will also contain some general analysis of the conjectures.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-09-11T20:36:37.000Z",
      "title": "Hindman's Theorem, Ellis's Lemma, and Thompson's group F",
      "abstract": "The purpose of this article is to formulate generalizations of Hindman's Theorem and Ellis's Lemma for non associative groupoids. A relation between these conjectures is proved and it is shown that they imply the amenability of Thompson's group F. In fact the amenability of F is equivalent to a finite form of the conjectured extension of Hindman's Theorem.",
      "comment": "This paper has been made obsolete by arXiv:1209.2063",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2018-07-16T16:52:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E02",
      "03E50",
      "05D10",
      "05C55",
      "20F38",
      "43A07"
    ],
    "keywords": [
      "hindmans theorem",
      "thompsons group",
      "elliss lemma",
      "formulate generalizations",
      "non associative groupoids"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.4735T"
    }
  }
}