{
  "id": "math/0703414",
  "version": "v1",
  "published": "2007-03-14T11:47:38.000Z",
  "updated": "2007-03-14T11:47:38.000Z",
  "title": "The octahedron recurrence and RSK-correspondence",
  "authors": [
    "V. I. Danilov",
    "G. A. Koshevoy"
  ],
  "comment": "16 pages, 6 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We start with an ``algebraic'' RSK-correspondence due to Noumi and Yamada. Given a matrix $X$, we consider a pyramidal array of solid minors of $X$. It turns out that this array satisfies an algebraic variant of octahedron recurrence. The main observation is that this array can also be constructed with the help of some square `genetic' array. Next we tropicalize this algebraic construction and consider $T$-{\\em polarized} pyramidal arrays (that is arrays satisfying octahedral relations). As a result we get several bijections, viz: a) a linear bijection between non-negative arrays and supermodular functions; b) a piecewise linear bijection between supermodular functions and the so called infra-modular functions; c) a linear bijection between infra-modular functions and plane partitions. A composition of these bijections yields a bijection between non-negative arrays and plane partitions coinciding with the modified RSK-correspondence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-14T11:47:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "octahedron recurrence",
      "rsk-correspondence",
      "pyramidal array",
      "plane partitions",
      "infra-modular functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3414D"
    }
  }
}