{
  "id": "math/9905094",
  "version": "v1",
  "published": "1999-05-17T10:42:40.000Z",
  "updated": "1999-05-17T10:42:40.000Z",
  "title": "Combinatorics of free cumulants",
  "authors": [
    "Bernadette Krawczyk",
    "Roland Speicher"
  ],
  "comment": "26 pages, Latex2e",
  "categories": [
    "math.CO",
    "math.OA",
    "math.PR"
  ],
  "abstract": "We derive a formula for expressing free cumulants whose entries are products of random variables in terms of the lattice structure of non-crossing partitions. We show the usefulness of that result by giving direct and conceptually simple proofs for a lot of results about $R$-diagonal elements. Our investigations do not assume the trace property for the considered linear functionals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-05-17T10:42:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combinatorics",
      "linear functionals",
      "trace property",
      "expressing free cumulants",
      "diagonal elements"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......5094K"
    }
  }
}