{
  "id": "2212.05091",
  "version": "v1",
  "published": "2022-12-09T19:28:52.000Z",
  "updated": "2022-12-09T19:28:52.000Z",
  "title": "Analysis of some exactly solvable diminishing urn models",
  "authors": [
    "Hsien-Kuei Hwang",
    "Markus Kuba",
    "Alois Panholzer"
  ],
  "comment": "11 pages, 2 figures; appeared in the Proceedings of the Formal Power Series and Algebraic Combinatorics (FPSAC 2007) Nankai University, Tianjin, China, 2007 (only printed proceedings). arXiv admin note: text overlap with arXiv:1110.2425",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We study several exactly solvable Polya-Eggenberger urn models with a \\emph{diminishing} character, namely, balls of a specified color, say $x$ are completely drawn after a finite number of draws. The main quantity of interest here is the number of balls left when balls of color $x$ are completely removed. We consider several diminishing urns studied previously in the literature such as the pills problem, the cannibal urns and the OK Corral problem, and derive exact and limiting distributions. Our approach is based on solving recurrences via generating functions and partial differential equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-09T19:28:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "60F05",
      "05C05"
    ],
    "keywords": [
      "exactly solvable diminishing urn models",
      "exactly solvable polya-eggenberger urn models",
      "ok corral problem",
      "partial differential equations",
      "finite number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}