{
  "id": "1403.7659",
  "version": "v2",
  "published": "2014-03-29T18:36:55.000Z",
  "updated": "2015-03-08T11:43:38.000Z",
  "title": "Substitution shifts generated by $p$-adic integer sequences",
  "authors": [
    "Eric Rowland",
    "Reem Yassawi"
  ],
  "comment": "17 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We set the stage for studying some substitution shifts defined on an infinite alphabet. We consider sequences of $p$-adic integers that project modulo $p^\\alpha$ to a $p$-automatic sequence for every $\\alpha \\geq 0$. Examples include algebraic sequences of integers, which satisfy this property for any prime $p$, and some cocycle sequences, which we show satisfy this property for a fixed $p$. By considering the shift-orbit closure of such a sequence in $\\mathbb{Z}_p^\\mathbb{N}$, we describe how this shift is a letter-to-letter coding of a shift generated by a constant-length substitution defined on an uncountable alphabet.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-29T18:36:55.000Z",
      "title": "A family of constant length substitutions on the p-adic integers",
      "abstract": "We set the stage for studying some substitution subshifts defined on an infinite alphabet. We consider sequences of $p$-adic integers that project modulo $p^\\alpha$ to a $p$-automatic sequence for every $\\alpha \\geq 1$. Examples include algebraic sequences of integers, which satisfy this property for any prime $p$, and some cocycle sequences, which we show satisfy this property for a fixed $p$. By considering the shift-orbit closure of such a sequence in ${\\mathbb Z}_p^{\\mathbb N}$, we describe how this subshift is a letter-to-letter coding of a subshift generated by a constant-length substitution defined on a closed subset of ${\\mathbb Z}_p$.",
      "comment": "16 pages, 5 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-03-08T11:43:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "05A15",
      "11A07",
      "11B85"
    ],
    "keywords": [
      "constant length substitutions",
      "p-adic integers",
      "project modulo",
      "substitution subshifts",
      "automatic sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.7659R"
    }
  }
}