{
  "id": "1801.04809",
  "version": "v1",
  "published": "2018-01-15T14:08:41.000Z",
  "updated": "2018-01-15T14:08:41.000Z",
  "title": "A partial order on Motzkin paths",
  "authors": [
    "Wenjie Fang"
  ],
  "comment": "13 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Tamari lattice, defined on Catalan objects such as binary trees and Dyck paths, is a well-studied object in combinatorics. It is thus natural to try to extend it to other family of lattice paths. In this article, we fathom such a possibility by defining and studying an analog of the Tamari lattice on Motzkin paths. We find that the defined partial order is not a lattice, but rather a disjoint union of components, each isomorphic to an interval in the classical Tamari lattice. With this structural result, we proceed to the enumeration of components and intervals in the poset of Motzkin paths we defined. We also extends the structural and enumerative results to Schr\\\"oder paths. At the end, we discuss the relation between our work and that of Baril and Pallo (2014).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-15T14:08:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "motzkin paths",
      "binary trees",
      "dyck paths",
      "lattice paths",
      "catalan objects"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}