{
  "id": "0908.1284",
  "version": "v1",
  "published": "2009-08-10T09:27:57.000Z",
  "updated": "2009-08-10T09:27:57.000Z",
  "title": "A new explicit formula for Kerov polynomials",
  "authors": [
    "P. Petrullo",
    "D. Senato"
  ],
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "We prove a formula expressing the Kerov polynomial $\\Sigma_k$ as a weighted sum over the lattice of noncrossing partitions of the set $\\{1,...,k+1\\}$. In particular, such a formula is related to a partial order $\\mirr$ on the Lehner's irreducible noncrossing partitions which can be described in terms of left-to-right minima and maxima, descents and excedances of permutations. This provides a translation of the formula in terms of the Cayley graph of the symmetric group $\\frak{S}_k$ and allows us to recover the coefficients of $\\Sigma_k$ by means of the posets $P_k$ and $Q_k$ of pattern-avoiding permutations discovered by B\\'ona and Simion. We also obtain symmetric functions specializing in the coefficients of $\\Sigma_k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-10T09:27:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "06A11",
      "05E05"
    ],
    "keywords": [
      "kerov polynomial",
      "explicit formula",
      "partial order",
      "lehners irreducible noncrossing partitions",
      "symmetric functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.1284P"
    }
  }
}