{
  "id": "math/0409447",
  "version": "v1",
  "published": "2004-09-23T09:43:27.000Z",
  "updated": "2004-09-23T09:43:27.000Z",
  "title": "A simple proof of associativity and commutativity of LR-coefficients (or the hive ring)",
  "authors": [
    "V. Danilov",
    "G. Koshevoy"
  ],
  "comment": "18 pages, 9 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a simple bijective proof of associativity and commutativity of the Littlewood-Richardson coefficients or the hive ring. Specifically, we establish existence a polarized polymatroidal discretely concave functions on the tetrahedron with given boundary values at two adjoint faces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-23T09:43:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple proof",
      "hive ring",
      "associativity",
      "commutativity",
      "lr-coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9447D"
    }
  }
}