{
  "id": "1604.03016",
  "version": "v1",
  "published": "2016-04-11T16:11:16.000Z",
  "updated": "2016-04-11T16:11:16.000Z",
  "title": "Face monoid actions and tropical hyperplane arrangements",
  "authors": [
    "Marianne Johnson",
    "Mark Kambites"
  ],
  "comment": "22 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study the combinatorics of tropical hyperplane arrangements, and their relationship to (classical) hyperplane face monoids. We show that the refinement operation on the faces of a tropical hyperplane arrangement, introduced by Ardila and Develin in their definition of a tropical oriented matroid, induces an action of the hyperplane face monoid of the classical braid arrangement on the arrangement, and hence on a number of interesting related structures. Along the way, we introduce a new characterization of the types (in the sense of Develin and Sturmfels) of points with respect to a tropical hyperplane arrangement, in terms of partial bijections which attain permanents of submatrices of a matrix which naturally encodes the arrangement.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-11T16:11:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A80",
      "52B12",
      "20M30"
    ],
    "keywords": [
      "tropical hyperplane arrangement",
      "face monoid actions",
      "hyperplane face monoid",
      "classical braid arrangement",
      "refinement operation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}