{
  "id": "1507.07370",
  "version": "v1",
  "published": "2015-07-27T11:38:50.000Z",
  "updated": "2015-07-27T11:38:50.000Z",
  "title": "Combinatorial properties of Nil-Bohr sets",
  "authors": [
    "Jakub Konieczny"
  ],
  "comment": "25 pages",
  "categories": [
    "math.NT",
    "math.CO",
    "math.DS"
  ],
  "abstract": "In this paper we study the relation between two notions of largeness that apply to a set of positive integers, namely $\\mathrm{Nil}_d{-}\\mathrm{Bohr}$ and $\\mathrm{SG}_k$, as introduced by Host and Kra. We prove that any $\\mathrm{Nil}_d{-}\\mathrm{Bohr}_0$ set is necessarily $\\mathrm{SG}_k$ where ${k}$ is effectively bounded in terms of $d$. This partially resolves a conjecture of Host and Kra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-27T11:38:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nil-bohr sets",
      "combinatorial properties",
      "conjecture",
      "positive integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}