{
  "id": "0705.2189",
  "version": "v1",
  "published": "2007-05-15T16:56:10.000Z",
  "updated": "2007-05-15T16:56:10.000Z",
  "title": "Combinatorial Hopf algebras and K-homology of Grassmanians",
  "authors": [
    "Thomas Lam",
    "Pavlo Pylyavskyy"
  ],
  "comment": "35 pages, 10 figures",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, we study six combinatorial Hopf algebras. These Hopf algebras can be thought of as K-theoretic analogues of the by now classical ``square'' of Hopf algebras consisting of symmetric functions, quasisymmetric functions, noncommutative symmetric functions and the Malvenuto-Reutenauer Hopf algebra of permutations. In addition, we develop a theory of set-valued P-partitions and study three new families of symmetric functions which are weight generating functions of reverse plane partitions, weak set-valued tableaux and valued-set tableaux.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-15T16:56:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "57T05",
      "14M15"
    ],
    "keywords": [
      "combinatorial hopf algebras",
      "grassmanians",
      "k-homology",
      "reverse plane partitions",
      "malvenuto-reutenauer hopf algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.2189L"
    }
  }
}