{
  "id": "1810.08235",
  "version": "v1",
  "published": "2018-10-18T18:50:31.000Z",
  "updated": "2018-10-18T18:50:31.000Z",
  "title": "On the unimodality of convolutions of sequences of binomial coefficients",
  "authors": [
    "Tricia Muldoon Brown"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We provide necessary and sufficient conditions on the unimodality of a convolution of two sequences of binomial coefficients preceded by a finite number of ones. These convolution sequences arise as as rank sequences of posets of vertex-induced subtrees for a particular class of trees. The number of such trees whose poset of vertex-induced subgraphs containing the root is not rank unimodal is determined for a fixed number of vertices $i$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-18T18:50:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "binomial coefficients",
      "unimodality",
      "convolution sequences arise",
      "rank sequences",
      "finite number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}