{
  "id": "2503.23182",
  "version": "v2",
  "published": "2025-03-29T18:34:47.000Z",
  "updated": "2025-05-06T19:18:55.000Z",
  "title": "A Resolution of the McCarty Conjecture",
  "authors": [
    "Anant Godbole",
    "Lybitina Koene",
    "Grant Shirley"
  ],
  "comment": "There appears to be an error in the proof of the main result",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "The McCarty Conjecture states that any McCarty Matrix (an $n\\times n$ matrix $A$ with positive integer entries and each of the $2n$ row and column sums equal to $n$), can be additively decomposed into two other matrices, $B$ and $C$, such that $B$ has row and column sumsets both equal to $\\{1, 2,... n\\}$, and $C$ has row and column sumsets both equal to $\\{0, 1,... n-1\\}$. The problem can also be formulated in terms of bipartite graphs. In this paper we use probabilistic methods to resolve this conjecture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-05-06T19:18:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "column sumsets",
      "resolution",
      "mccarty conjecture states",
      "column sums equal",
      "probabilistic methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}