{
  "id": "2105.14542",
  "version": "v1",
  "published": "2021-05-30T13:43:44.000Z",
  "updated": "2021-05-30T13:43:44.000Z",
  "title": "Enumerating chambers of hyperplane arrangements with symmetry",
  "authors": [
    "Taylor Brysiewicz",
    "Holger Eble",
    "Lukas Kühne"
  ],
  "comment": "19 pages, 6 figures, 8 tables, 1 appendix",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce a new algorithm for enumerating chambers of hyperplane arrangements which exploits their underlying symmetry groups. Our algorithm counts the chambers of an arrangement as a byproduct of computing its characteristic polynomial. We showcase our julia implementation, based on OSCAR, on examples coming from hyperplane arrangements with applications to physics and computer science.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-30T13:43:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C35",
      "52B15",
      "G.2.1"
    ],
    "keywords": [
      "hyperplane arrangements",
      "enumerating chambers",
      "algorithm counts",
      "computer science",
      "characteristic polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}