{
  "id": "1409.2354",
  "version": "v1",
  "published": "2014-09-08T14:17:20.000Z",
  "updated": "2014-09-08T14:17:20.000Z",
  "title": "Constructions of words rich in palindromes and pseudopalindromes",
  "authors": [
    "Edita Pelantová",
    "Štěpán Starosta"
  ],
  "comment": "28 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A narrow connection between infinite binary words rich in classical palindromes and infinite binary words rich simultaneously in palindromes and pseudopalindromes (the so-called $H$-rich words) is demonstrated. The correspondence between rich and $H$-rich words is based on the operation $S$ acting over words over the alphabet $\\{0,1\\}$ and defined by $S(u_0u_1u_2\\ldots) = v_1v_2v_3\\ldots$, where $v_i= u_{i-1} + u_i \\mod 2$. The operation $S$ enables us to construct a new class of rich words and a new class of $H$-rich words. Finally, the operation $S$ is considered on the multiliteral alphabet $\\mathbb{Z}_m$ as well and applied to the generalized Thue--Morse words. As a byproduct, new binary rich and $H$-rich words are obtained by application of $S$ on the generalized Thue--Morse words over the alphabet $\\mathbb{Z}_4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-08T14:17:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R15"
    ],
    "keywords": [
      "rich words",
      "pseudopalindromes",
      "generalized thue-morse words",
      "constructions",
      "infinite binary words rich"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.2354P"
    }
  }
}