{
  "id": "1705.02497",
  "version": "v1",
  "published": "2017-05-06T16:13:14.000Z",
  "updated": "2017-05-06T16:13:14.000Z",
  "title": "Pascal Triangle and Restricted Words",
  "authors": [
    "Milan Janjic"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We continue to investigate combinatorial properties of functions $f_m$ and $c_m$ considered in our previous papers. They depend on an initial arithmetic function $f_0$. In this paper, the values of $f_0$ are the binomial coefficients. We first consider the case when the values of $f_0$ are the binomial coefficients from a row of the Pascal triangle. The values of $f_0$ consider next are the binomial coefficients from a diagonal of the Pascal triangle. In two final cases, the values of $f_0$ are the central binomial coefficients and its adjacent neighbors. In each case, we derive an explicit formula for $c_1(n,k)$ and give its interpretation in terms of restricted words. In the first two cases, we also consider the functions $f_m$ and $c_m$, for $(m>0)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-06T16:13:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pascal triangle",
      "restricted words",
      "initial arithmetic function",
      "central binomial coefficients",
      "explicit formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}