{
  "id": "math-ph/0304004",
  "version": "v1",
  "published": "2003-04-01T10:12:16.000Z",
  "updated": "2003-04-01T10:12:16.000Z",
  "title": "3-enumerated alternating sign matrices",
  "authors": [
    "Yu. G. Stroganov"
  ],
  "comment": "13 pages",
  "categories": [
    "math-ph",
    "math.CO",
    "math.MP"
  ],
  "abstract": "Let $A(n,r;3)$ be the total weight of the alternating sign matrices of order $n$ whose sole `1' of the first row is at the $r^{th}$ column and the weight of an individual matrix is $3^k$ if it has $k$ entries equal to -1. Define the sequence of the generating functions $G_n(t)=\\sum_{r=1}^n A(n,r;3)t^{r-1}$. Results of two different kind are obtained. On the one hand I made the explicit expression for the even subsequence $G_{2\\nu}(t)$ in terms of two linear homogeneous second order recurrence in $\\nu$ (Theorem 1). On the other hand I brought to light the nice connection between the neighbouring functions $G_{2\\nu+1}(t)$ and $G_{2\\nu}(t)$ (Theorem 2). The 3-enumeration $A(n;3) \\equiv G_n(1)$ which was found by Kuperberg is reproduced as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-04-01T10:12:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "alternating sign matrices",
      "linear homogeneous second order recurrence",
      "nice connection",
      "first row",
      "individual matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.ph...4004S"
    }
  }
}