{
  "id": "2309.01704",
  "version": "v1",
  "published": "2023-09-04T16:29:20.000Z",
  "updated": "2023-09-04T16:29:20.000Z",
  "title": "A Note on the Union-closed Sets Conjecture",
  "authors": [
    "Mohammad Javad Moghaddas Mehr"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $M=(m_{ij})$ be a binary matrix of size $n \\times m$ with distinct rows where its rows are closed under logical operators such as \"$\\boldsymbol{\\rightarrow}$\", \"$\\boldsymbol{\\land}$\", \"$\\boldsymbol{\\neg}$\", etc. In this article, we explore whether, in each case, there exists a column that has an equal or greater number of ones than zeros.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-04T16:29:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "03E05"
    ],
    "keywords": [
      "union-closed sets conjecture",
      "greater number",
      "binary matrix",
      "distinct rows",
      "logical operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}