{
  "id": "2311.07181",
  "version": "v1",
  "published": "2023-11-13T09:14:31.000Z",
  "updated": "2023-11-13T09:14:31.000Z",
  "title": "Two New Integer Sequences Related to Crossroads and Catalan Numbers",
  "authors": [
    "Julien Rouyer",
    "Alain Ninet"
  ],
  "comment": "Submitted to the Journal of Integer Sequences on November 11, 2023",
  "categories": [
    "math.CO"
  ],
  "abstract": "The lonely singles sequence represents the number of noncrossing partitions of the finite set {1,. .. , n} in which no pair of singletons {i} and {j} can be merged into the pair {i, j} so that the partition stays noncrossing. The marriageable singles sequence represents the number of all the other noncrossing partitions and is the difference between the Catalan numbers sequence and the lonely singles sequence. The 14 first terms of these sequences are given, as well as some of their properties. These sequences appear when one wants to count the number of ways to cross simultaneously certain road intersections.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-13T09:14:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integer sequences",
      "crossroads",
      "lonely singles sequence represents",
      "catalan numbers sequence",
      "marriageable singles sequence represents"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}