{
  "id": "1706.07213",
  "version": "v1",
  "published": "2017-06-22T08:51:53.000Z",
  "updated": "2017-06-22T08:51:53.000Z",
  "title": "Restricted inversion sequences and enhanced $3$-noncrossing partitions",
  "authors": [
    "Zhicong Lin"
  ],
  "comment": "10 pages, presented at the S\\'eminaire de Combinatoire et Th\\'eorie des Nombres at Institut Camille Jordan in 21 March, 2017. This version was submitted to Eur-JC in March, 2017",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove a conjecture due independently to Yan and Martinez-Savage that asserts inversion sequences with no weakly decreasing subsequence of length $3$ and enhanced $3$-noncrossing partitions have the same cardinality. Our approach applies both the generating tree technique and the so-called obstinate kernel method developed by Bousquet-M\\'elou. One application of this equinumerosity is a discovery of an intriguing identity involving numbers of classical and enhanced $3$-noncrossing partitions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-22T08:51:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "noncrossing partitions",
      "restricted inversion sequences",
      "obstinate kernel method",
      "asserts inversion sequences",
      "generating tree technique"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}