{
  "id": "1009.4750",
  "version": "v3",
  "published": "2010-09-24T02:06:44.000Z",
  "updated": "2010-11-11T18:41:13.000Z",
  "title": "Triangulations of $Δ_{n-1} \\times Δ_{d-1}$ and Tropical Oriented Matroids",
  "authors": [
    "Suho Oh",
    "Hwanchul Yoo"
  ],
  "comment": "11 pages and 3 figures. Any comment or feedback would be welcomed v2. Our result is that triangulations of product of simplices is a tropical oriented matroid. We are trying to extend this to all subdivisions. v3 Replaces the proof of Lemma 2.6 with a reference.. Proof of the matrix being totally unimodular is now more detailed. Extended abstract will be submitted to FPSAC '11",
  "categories": [
    "math.CO"
  ],
  "abstract": "Develin and Sturmfels showed that regular triangulations of $\\Delta_{n-1} \\times \\Delta_{d-1}$ can be thought as tropical polytopes. Tropical oriented matroids were defined by Ardila and Develin, and were conjectured to be in bijection with all subdivisions of $\\Delta_{n-1} \\times \\Delta_{d-1}$. In this paper, we show that any triangulation of $\\Delta_{n-1} \\times \\Delta_{d-1}$ encodes a tropical oriented matroid. We also suggest a new class of combinatorial objects that may describe all subdivisions of a bigger class of polytopes.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-11-11T18:41:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tropical oriented matroid",
      "bigger class",
      "combinatorial objects",
      "regular triangulations",
      "subdivisions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.4750O"
    }
  }
}