{
  "id": "0906.3999",
  "version": "v2",
  "published": "2009-06-22T13:20:26.000Z",
  "updated": "2009-09-22T13:36:09.000Z",
  "title": "Shapes of RNA pseudoknot structures",
  "authors": [
    "Christian M. Reidys",
    "Rita R. Wang"
  ],
  "comment": "24 pages, 7 figures,",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we study abstract shapes of $k$-noncrossing, $\\sigma$-canonical RNA pseudoknot structures. We consider ${\\sf lv}_k^{\\sf 1}$- and ${\\sf lv}_k^{\\sf 5}$-shapes, which represent a generalization of the abstract $\\pi'$- and $\\pi$-shapes of RNA secondary structures introduced by \\citet{Giegerich:04ashape}. Using a novel approach we compute the generating functions of ${\\sf lv}_k^{\\sf 1}$- and ${\\sf lv}_k^{\\sf 5}$-shapes as well as the generating functions of all ${\\sf lv}_k^{\\sf 1}$- and ${\\sf lv}_k^{\\sf 5}$-shapes induced by all $k$-noncrossing, $\\sigma$-canonical RNA structures for fixed $n$. By means of singularity analysis of the generating functions, we derive explicit asymptotic expressions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-09-22T13:36:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16"
    ],
    "keywords": [
      "generating functions",
      "canonical rna pseudoknot structures",
      "derive explicit asymptotic expressions",
      "rna secondary structures",
      "study abstract shapes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.3999R"
    }
  }
}