{
  "id": "0903.5073",
  "version": "v2",
  "published": "2009-03-29T17:22:49.000Z",
  "updated": "2009-04-15T09:06:15.000Z",
  "title": "More refined enumerations of alternating sign matrices",
  "authors": [
    "Ilse Fischer",
    "Dan Romik"
  ],
  "comment": "38 pages; added references and made minor changes to the introduction; source files now inlcude the Mathematica package RefinedASM",
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study a further refinement of the standard refined enumeration of alternating sign matrices (ASMs) according to their first two rows instead of just the first row, and more general \"d-refined\" enumerations of ASMs according to the first d rows. For the doubly-refined case of d=2, we derive a system of linear equations satisfied by the doubly-refined enumeration numbers A_{n,i,j} that enumerate such matrices. We give a conjectural explicit formula for A_{n,i,j} and formulate several other conjectures about the sufficiency of the linear equations to determine the A_{n,i,j}'s and about an extension of the linear equations to the general d-refined enumerations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-04-15T09:06:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15"
    ],
    "keywords": [
      "alternating sign matrices",
      "linear equations",
      "conjectural explicit formula",
      "general d-refined enumerations"
    ],
    "tags": [
      "research tool"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.5073F"
    }
  }
}