{
  "id": "2202.04938",
  "version": "v1",
  "published": "2022-02-10T10:11:35.000Z",
  "updated": "2022-02-10T10:11:35.000Z",
  "title": "A full characterization of Bertrand numeration systems",
  "authors": [
    "Émilie Charlier",
    "Célia Cisternino",
    "Manon Stipulanti"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Among all positional numeration systems, the widely studied Bertrand numeration systems are defined by a simple criterion in terms of their numeration languages. In 1989, Bertrand-Mathis characterized them via representations in a real base $\\beta$. However, the given condition turns to be not necessary. Hence, the goal of this paper is to provide a correction of Bertrand-Mathis' result. The main difference arises when $\\beta$ is a Parry number, in which case are derived two associated Bertrand numeration systems. Along the way, we define a non-canonical $\\beta$-shift and study its properties analogously to those of the usual canonical one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-10T10:11:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "full characterization",
      "positional numeration systems",
      "associated bertrand numeration systems",
      "main difference arises",
      "bertrand-mathis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}