{
  "id": "math/0512366",
  "version": "v1",
  "published": "2005-12-15T15:37:46.000Z",
  "updated": "2005-12-15T15:37:46.000Z",
  "title": "Enriched $P$-partitions and peak algebras (extended abstract)",
  "authors": [
    "T. Kyle Petersen"
  ],
  "comment": "12 pages, 4 figures. Shortened version of math.CO/0508041",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "abstract": "We generalize Stembridge's enriched $P$-partitions and use this theory to outline the structure of peak algebras for the symmetric group and the hyperoctahedral group. Whereas Stembridge's enriched $P$-partitions are related to quasisymmetric functions (the coalgebra dual to Solomon's type A descent algebra), our generalized enriched $P$-partitions are related to type B quasisymmetric functions (the coalgebra dual to Solomon's type B descent algebra). Using these functions, we explore three different peak algebras: the \"interior\" and \"left\" peak algebras of type A, and a new type B peak algebra. Our results specialize to results for commutative peak algebras as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-15T15:37:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E99",
      "20F55",
      "06A07"
    ],
    "keywords": [
      "extended abstract",
      "partitions",
      "solomons type",
      "quasisymmetric functions",
      "coalgebra dual"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12366P"
    }
  }
}