{
  "id": "1405.3626",
  "version": "v2",
  "published": "2014-05-14T19:08:58.000Z",
  "updated": "2014-06-06T12:04:15.000Z",
  "title": "Arithmetic Properties of Andrews' Singular Overpartitions",
  "authors": [
    "Shi-Chao Chen",
    "Michael D. Hirschhorn",
    "James A. Sellers"
  ],
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "In a very recent work, G. E. Andrews defined the combinatorial objects which he called {\\it singular overpartitions} with the goal of presenting a general theorem for overpartitions which is analogous to theorems of Rogers--Ramanujan type for ordinary partitions with restricted successive ranks. As a small part of his work, Andrews noted two congruences modulo 3 which followed from elementary generating function manipulations. In this work, we prove that Andrews' results modulo 3 are two examples of an infinite family of congruences modulo 3 which hold for that particular function. We also expand the consideration of such arithmetic properties to other functions which are part of Andrews' framework for singular overpartitions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-06T12:04:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P83"
    ],
    "keywords": [
      "singular overpartitions",
      "arithmetic properties",
      "congruences modulo",
      "elementary generating function manipulations",
      "small part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.3626C"
    }
  }
}