{
  "id": "1707.07798",
  "version": "v1",
  "published": "2017-07-25T02:59:14.000Z",
  "updated": "2017-07-25T02:59:14.000Z",
  "title": "$(an+b)$-color compositions",
  "authors": [
    "Daniel Birmajer",
    "Juan B. Gil",
    "Michael D. Weiner"
  ],
  "comment": "Submitted to the Proceedings of the 48th Southeastern International Conference on Combinatorics, Graph Theory & Computing",
  "categories": [
    "math.CO"
  ],
  "abstract": "For $a,b\\in\\mathbb{N}_0$, we consider $(an+b)$-color compositions of a positive integer $\\nu$ for which each part of size $n$ admits $an+b$ colors. We study these compositions from the enumerative point of view and give a formula for the number of $(an+b)$-color compositions of $\\nu$ with $k$ parts. Our formula is obtained in two different ways: 1) by means of algebraic properties of partial Bell polynomials, and 2) through a bijection to a certain family of weak compositions that we call domino compositions. We also discuss two cases when $b$ is negative and give corresponding combinatorial interpretations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-25T02:59:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A19"
    ],
    "keywords": [
      "color compositions",
      "partial bell polynomials",
      "algebraic properties",
      "weak compositions",
      "domino compositions"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}