{
  "id": "1511.08788",
  "version": "v1",
  "published": "2015-11-27T20:49:12.000Z",
  "updated": "2015-11-27T20:49:12.000Z",
  "title": "On the length of fully commutative elements",
  "authors": [
    "Philippe Nadeau"
  ],
  "comment": "19 pages",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "abstract": "In a Coxeter group $W$, an element is fully commutative if any two of its reduced expressions can be linked by a series of commutation of adjacent letters. These elements have particularly nice combinatorial properties, and also index a basis of the generalized Temperley--Lieb algebra attached to $W$. We give two results about the sequence counting these elements with respect to their Coxeter length. First we prove that it always satisfies a linear recurrence with constant coefficients, by showing that reduced expressions of fully commutative elements form a regular language. Then we classify those groups $W$ for which the sequence is ultimately periodic, extending a result of Stembridge. These results are applied to the growth of generalized Temperley--Lieb algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-27T20:49:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fully commutative elements",
      "generalized temperley-lieb algebra",
      "reduced expressions",
      "particularly nice combinatorial properties",
      "coxeter length"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151108788N"
    }
  }
}