{
  "id": "math-ph/0312021",
  "version": "v1",
  "published": "2003-12-09T13:09:53.000Z",
  "updated": "2003-12-09T13:09:53.000Z",
  "title": "Construction of some special subsequences within a Farey sequence",
  "authors": [
    "B. Basu-Mallick",
    "Tanaya Bhattacharyya",
    "Diptiman Sen"
  ],
  "comment": "latex, 8 pages",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "math.NT",
    "nlin.SI"
  ],
  "abstract": "Recently it has been found that some special subsequences within a Farey sequence play a crucial role in determining the ranges of coupling constant for which quantum soliton states can exist for an integrable derivative nonlinear Schrodinger model. In this article, we find a novel mapping which connects two such subsequences belonging to Farey sequences of different orders. By using this mapping, we construct an algorithm to generate all of these special subsequences within a Farey sequence. We also derive the continued fraction expansions for all the elements belonging to a subsequence and observe a close connection amongst the corresponding expansion coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-12-09T13:09:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "special subsequences",
      "construction",
      "integrable derivative nonlinear schrodinger model",
      "quantum soliton states",
      "farey sequence play"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 635283,
      "adsabs": "2003math.ph..12021B"
    }
  }
}