{
  "id": "math/0306110",
  "version": "v1",
  "published": "2003-06-06T01:20:10.000Z",
  "updated": "2003-06-06T01:20:10.000Z",
  "title": "A sign-reversing involution for rooted special rim-hook tableaux",
  "authors": [
    "Bruce E. Sagan",
    "Jaejin Lee"
  ],
  "comment": "13 pages, 6 figures, Latex see related papers at http://www.math.msu.edu/~sagan",
  "categories": [
    "math.CO"
  ],
  "abstract": "Egecioglu and Remmel gave an interpretation for the entries of the inverse Kostka matrix K^{-1} in terms of special rim-hook tableaux. They were able to use this interpretation to give a combinatorial proof that KK^{-1}=I but were unable to do the same for the equation K^{-1}K=I. We define a sign-reversing involution on rooted special rim-hook tableaux which can be used to prove that the last column of this second product is correct. In addition, following a suggestion of Chow we combine our involution with a result of Gasharov to give a combinatorial proof of a special case of the (3+1)-free Conjecture of Stanley and Stembridge.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-06-06T01:20:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "05A17",
      "05E05",
      "06A11"
    ],
    "keywords": [
      "rooted special rim-hook tableaux",
      "sign-reversing involution",
      "combinatorial proof",
      "inverse kostka matrix",
      "remmel gave"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......6110S"
    }
  }
}