{
  "id": "math/0607570",
  "version": "v5",
  "published": "2006-07-24T19:06:00.000Z",
  "updated": "2009-07-12T19:17:02.000Z",
  "title": "Pattern Recognition on Oriented Matroids: The Existence of a Tope Committee",
  "authors": [
    "Andrey O. Matveev"
  ],
  "comment": "40 pages, 12 figures; v.2 - corrections in Section 5.2, references added; v.3,4,5 - minor improvements and reorganization",
  "categories": [
    "math.CO"
  ],
  "abstract": "Oriented matroids can serve as a tool of modeling of collective decision-making processes in contradictory problems of pattern recognition. We present a generalization of the committee techniques of pattern recognition to oriented matroids. A tope committee for an oriented matroid is a subset of its maximal covectors such that every positive halfspace contains more than half of the maximal covectors from this subset. For a large subfamily of oriented matroids their committee structure is quite rich; for example, any maximal chains in their tope posets provide one with information sufficient to construct a committee.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2009-07-12T19:17:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C35",
      "52C40",
      "68T10",
      "90C27"
    ],
    "keywords": [
      "oriented matroid",
      "pattern recognition",
      "tope committee",
      "maximal covectors",
      "positive halfspace contains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7570M"
    }
  }
}