{
  "id": "math/0612369",
  "version": "v7",
  "published": "2006-12-13T20:16:39.000Z",
  "updated": "2008-11-30T18:38:41.000Z",
  "title": "Pattern Recognition on Oriented Matroids: Layers of Tope Committees",
  "authors": [
    "Andrey O. Matveev"
  ],
  "comment": "15 pages; v.2,3 - introductory section and misprints in section 5 corrected; v.4,5 - minor improvements; v.6 - connection of Section 3 with INTEGERS 7 (2007) #20 described; v.7 - Proposition 4.1 and Theorem 5.1 reformulated, other minor changes in text and references",
  "categories": [
    "math.CO"
  ],
  "abstract": "A tope committee K* for a simple oriented matroid M is a subset of its maximal covectors such that every positive halfspace of M contains more than half of the covectors from K*. The structures of the family of all committees for M, and of the family of its committees that contain no pairs of opposites, are described. A Farey subsequence associated with the elements of the m-th layer of the Boolean lattice of rank 2m is explored.",
  "revisions": [
    {
      "version": "v7",
      "updated": "2008-11-30T18:38:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E30",
      "11B57",
      "52C35",
      "52C40",
      "68T10",
      "90C27"
    ],
    "keywords": [
      "tope committee",
      "pattern recognition",
      "maximal covectors",
      "simple oriented matroid",
      "m-th layer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12369M"
    }
  }
}