{
  "id": "0801.4069",
  "version": "v1",
  "published": "2008-01-26T10:35:27.000Z",
  "updated": "2008-01-26T10:35:27.000Z",
  "title": "The morphology of infinite tournaments. Application to the growth of their profile",
  "authors": [
    "Youssef Boudabbous",
    "Maurice Pouzet"
  ],
  "comment": "25 pages, presented at CGCS 2007(Luminy, France, May 2-4 2007) in honor of Michel Deza",
  "categories": [
    "math.CO"
  ],
  "abstract": "A tournament is \\emph{acyclically indecomposable} if no acyclic autonomous set of vertices has more than one element. We identify twelve infinite acyclically indecomposable tournaments and prove that every infinite acyclically indecomposable tournament contains a subtournament isomorphic to one of these tournaments. The {\\it profile} of a tournament $T$ is the function $\\phi_T$ which counts for each integer $n$ the number $\\phi_T(n)$ of tournaments induced by $T$ on the $n$-element subsets of $T$, isomorphic tournaments being identified. As a corollary of the result above we deduce that the growth of $\\phi_T$ is either polynomial, in which case $\\phi_T(n)\\simeq an^k$, for some positive real $a$, some non-negative integer $k$, or as fast as some exponential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-26T10:35:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16",
      "05C20"
    ],
    "keywords": [
      "infinite tournaments",
      "application",
      "morphology",
      "infinite acyclically indecomposable tournament contains",
      "isomorphic tournaments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.4069B"
    }
  }
}