{
  "id": "1407.1297",
  "version": "v1",
  "published": "2014-07-04T19:01:01.000Z",
  "updated": "2014-07-04T19:01:01.000Z",
  "title": "Congruences of concave composition functions",
  "authors": [
    "Keenan Monks",
    "Lynnelle Ye"
  ],
  "comment": "7 pages; preprint of article published in INTEGERS",
  "journal": "Integers Journal (2013) vol. 13",
  "categories": [
    "math.NT"
  ],
  "abstract": "Concave compositions are ordered partitions whose parts are decreasing towards a central part. We study the distribution modulo $a$ of the number of concave compositions. Let $c(n)$ be the number of concave compositions of $n$ having even length. It is easy to see that $c(n)$ is even for all $n\\geq1$. Refining this fact, we prove that $$\\#\\{n<X:c(n)\\equiv 0\\pmod 4\\}\\gg\\sqrt{X}$$ and also that for every $a>2$ and at least two distinct values of $r\\in\\{0,1,\\dotsc,a-1\\}$, $$\\#\\{n<X: c(n)\\equiv r\\pmod{a}\\} > \\frac{\\log_2\\log_3 X}{a}.$$ We obtain similar results for concave compositions of odd length.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-04T19:01:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P83"
    ],
    "keywords": [
      "concave composition functions",
      "congruences",
      "similar results",
      "distinct values",
      "central part"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.1297M"
    }
  }
}