{
  "id": "2208.06841",
  "version": "v1",
  "published": "2022-08-14T12:15:53.000Z",
  "updated": "2022-08-14T12:15:53.000Z",
  "title": "On the cancellation-free antipode formula for the Malvenuto-Reutenauer Hopf Algebra",
  "authors": [
    "Da Xu",
    "Houyi Yu"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "abstract": "For the Malvenuto-Reutenauer Hopf algebra of permutations, we provide a cancellation-free antipode formula for permutations starting with a decreasing sequence consisting of two positive integers and ending with an increasing one. As a consequence, we confirm two conjectures posed by Carolina Benedetti and Bruce E. Sagan.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-14T12:15:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16T30",
      "05E05"
    ],
    "keywords": [
      "malvenuto-reutenauer hopf algebra",
      "cancellation-free antipode formula",
      "permutations",
      "carolina benedetti",
      "conjectures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}