{
  "id": "1703.04508",
  "version": "v1",
  "published": "2017-03-13T17:49:13.000Z",
  "updated": "2017-03-13T17:49:13.000Z",
  "title": "Pattern Recognition on Oriented Matroids: Decompositions of Topes, and Dehn-Sommerville Type Relations",
  "authors": [
    "Andrey O. Matveev"
  ],
  "comment": "5 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "If V(R) is the vertex set of a symmetric cycle R in the tope graph of a simple oriented matroid M, then for any tope T of M there exists a unique inclusion-minimal subset Q(T;R) of V(R) such that T is the sum of the topes of Q(T;R). If |Q(T;R)|>3, then the decomposition Q(T;R) of the tope T with respect to the symmetric cycle R satisfies certain Dehn-Sommerville type relations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-13T17:49:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dehn-sommerville type relations",
      "pattern recognition",
      "decomposition",
      "symmetric cycle",
      "unique inclusion-minimal subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}