{
  "id": "1603.09365",
  "version": "v1",
  "published": "2016-03-30T20:21:54.000Z",
  "updated": "2016-03-30T20:21:54.000Z",
  "title": "Gowers' Ramsey theorem for generalized tetris operations",
  "authors": [
    "Martino Lupini"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove a generalization of Gowers' theorem for $\\mathrm{FIN}_{k}$ where, instead of the single tetris operation $T:\\mathrm{FIN}_{k}\\rightarrow \\mathrm{FIN}_{k-1}$, one considers all maps from $\\mathrm{FIN}_{k}$ to $\\mathrm{FIN}_{j}$ for $0\\leq j\\leq k$ arising from nondecreasing surjections $f:\\left\\{ 0,1,\\ldots ,k+1\\right\\} \\rightarrow \\left\\{ 0,1,\\ldots ,j+1\\right\\} $. This answers a question of Barto\\v{s}ov\\'{a} and Kwiatkowska. We also prove a common generalization of such a result and the Galvin--Glazer--Hindman theorem on finite products, in the setting of layered partial semigroups introduced by Farah, Hindman, and McLeod.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-30T20:21:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D10",
      "54D80"
    ],
    "keywords": [
      "generalized tetris operations",
      "ramsey theorem",
      "single tetris operation",
      "common generalization",
      "galvin-glazer-hindman theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160309365L"
    }
  }
}