{
  "id": "math/0507210",
  "version": "v1",
  "published": "2005-07-11T08:55:41.000Z",
  "updated": "2005-07-11T08:55:41.000Z",
  "title": "Catalan-like numbers and succession rules",
  "authors": [
    "Luca Ferrari",
    "Renzo Pinzani"
  ],
  "comment": "Submitted. The paper has been presented at the conference \"Paths, Permutations and Trees\", held in Tianjin, 2004, February, 25-27",
  "categories": [
    "math.CO"
  ],
  "abstract": "The ECO method and the theory of Catalan-like numbers introduced by Aigner seems two completely unrelated combinatorial settings. In this work we try to establish a bridge between them, aiming at starting a (hopefully) fruitful study on their interactions. We show that, in a linear algebra context (more precisely, using infinite matrices), a succession rule can be translated into a (generalized) Aigner matrix by means of a suitable change of basis in the vector space of one-variable polynomials. We provide some examples to illustrate this fact and apply it to the study of two particular classes of succession rules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-11T08:55:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A10",
      "15A36"
    ],
    "keywords": [
      "succession rule",
      "catalan-like numbers",
      "linear algebra context",
      "vector space",
      "eco method"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7210F"
    }
  }
}