{
  "id": "1111.1251",
  "version": "v3",
  "published": "2011-11-04T21:10:36.000Z",
  "updated": "2013-09-23T06:03:35.000Z",
  "title": "On a Generalization of Zaslavsky's Theorem for Hyperplane Arrangements",
  "authors": [
    "Priyavrat Deshpande"
  ],
  "comment": "version 3: The title had a typo in v2 which is now fixed. Will appear in Annals of Combinatorics. Version. 2: 19 pages, major revision in terms of style and language, some results improved, contact information updated, final version",
  "journal": "Annals of Combinatorics, March 2014, Volume 18, Issue 1, pp 35-55",
  "doi": "10.1007/s00026-013-0210-9",
  "categories": [
    "math.CO",
    "math.AT"
  ],
  "abstract": "We define arrangements of codimension-1 submanifolds in a smooth manifold which generalize arrangements of hyperplanes. When these submanifolds are removed the manifold breaks up into regions, each of which is homeomorphic to an open disc. The aim of this paper is to derive formulas that count the number of regions formed by such an arrangement. We achieve this aim by generalizing Zaslavsky's theorem to this setting. We show that this number is determined by the combinatorics of the intersections of these submanifolds.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-09-23T06:03:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C35",
      "52B45",
      "05E45",
      "05A99",
      "57Q15"
    ],
    "keywords": [
      "hyperplane arrangements",
      "generalization",
      "submanifolds",
      "define arrangements",
      "manifold breaks"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.1251D"
    }
  }
}