{
  "id": "math/0508149",
  "version": "v1",
  "published": "2005-08-08T18:17:40.000Z",
  "updated": "2005-08-08T18:17:40.000Z",
  "title": "A note on three types of quasisymmetric functions",
  "authors": [
    "T. Kyle Petersen"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In the context of generating functions for $P$-partitions, we revisit three flavors of quasisymmetric functions: Gessel's quasisymmetric functions, Chow's type B quasisymmetric functions, and Poirier's signed quasisymmetric functions. In each case we use the inner coproduct to give a combinatorial description (counting pairs of permutations) to the multiplication in: Solomon's type A descent algebra, Solomon's type B descent algebra, and the Mantaci-Reutenauer algebra, respectively. The presentation is brief and elementary, our main results coming as consequences of $P$-partition theorems already in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-08-08T18:17:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E99"
    ],
    "keywords": [
      "descent algebra",
      "solomons type",
      "gessels quasisymmetric functions",
      "poiriers signed quasisymmetric functions",
      "partition theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......8149P"
    }
  }
}