{
  "id": "1207.7295",
  "version": "v1",
  "published": "2012-07-31T15:51:33.000Z",
  "updated": "2012-07-31T15:51:33.000Z",
  "title": "Unimodality and Dyck paths",
  "authors": [
    "Luca Ferrari"
  ],
  "comment": "15 pages. To appear on Journal of Combinatorial Mathematics and Combinatorial Computing",
  "categories": [
    "math.CO"
  ],
  "abstract": "We propose an original approach to the problem of rankunimodality for Dyck lattices. It is based on a well known recursive construction of Dyck paths originally developed in the context of the ECO methodology, which provides a partition of Dyck lattices into saturated chains. Even if we are not able to prove that Dyck lattices are rank-unimodal, we describe a family of polynomials (which constitutes a polynomial analog of ballot numbers) and a succession rule which appear to be useful in addressing such a problem. At the end of the paper, we also propose and begin a systematic investigation of the problem of unimodality of succession rules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-31T15:51:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dyck paths",
      "dyck lattices",
      "succession rule",
      "original approach",
      "systematic investigation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.7295F"
    }
  }
}