{
  "id": "2106.08257",
  "version": "v1",
  "published": "2021-06-15T16:03:58.000Z",
  "updated": "2021-06-15T16:03:58.000Z",
  "title": "Noncommutative Symmetric Functions and Lagrange Inversion II: Noncrossing partititions and the Farahat-Higman algebra",
  "authors": [
    "Jean-Christophe Novelli",
    "Jean-Yves Thibon"
  ],
  "comment": "35 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce a new pair of mutually dual bases of noncommutative symmetric functions and quasi-symmetric functions, and use it to derive generalizations of several results on the reduced incidence algebra of the lattice of noncrossing partitions. As a consequence, we obtain a quasi-symmetric version of the Farahat-Higman algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-15T16:03:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05"
    ],
    "keywords": [
      "noncommutative symmetric functions",
      "farahat-higman algebra",
      "lagrange inversion",
      "noncrossing partititions",
      "mutually dual bases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}