{
  "id": "1111.3142",
  "version": "v1",
  "published": "2011-11-14T08:57:10.000Z",
  "updated": "2011-11-14T08:57:10.000Z",
  "title": "Fibonacci-like growth of numerical semigroups of a given genus",
  "authors": [
    "Alex Zhai"
  ],
  "comment": "30 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give an asymptotic estimate of the number of numerical semigroups of a given genus. In particular, if $n_g$ is the number of numerical semigroups of genus $g$, we prove that $n_g$ tends to $S \\phi^g$, where $\\phi$ is the golden ratio, and $S$ is a constant, resolving several related conjectures concerning the growth of $n_g$. In addition, we show that the proportion of numerical semigroups of genus $g$ satisfying $f < 3m$ approaches 1 as $g \\rightarrow \\infty$, where $m$ is the multiplicity and $f$ is the Frobenius number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-14T08:57:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "numerical semigroups",
      "fibonacci-like growth",
      "asymptotic estimate",
      "frobenius number",
      "golden ratio"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.3142Z"
    }
  }
}