{
  "id": "2412.06379",
  "version": "v1",
  "published": "2024-12-09T10:58:09.000Z",
  "updated": "2024-12-09T10:58:09.000Z",
  "title": "Sign pattern matrices associated with cycle graphs that require algebraic positivity",
  "authors": [
    "Sunil Das"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A real matrix is said to be positive if its every entry is positive, and a real square matrix A is algebraically positive if there exists a real polynomial f such that f(A) is a positive matrix. A sign pattern matrix A is said to require a property if all matrices having sign pattern as A have that property. In this paper, we characterize all sign pattern matrices associated with cycle graphs having only negative 2-cycles that require algebraic positivity. We also give some necessary conditions for a sign pattern matrix to require algebraic positivity, and some sufficient conditions for a sign pattern matrix with cycle graph to require algebraic positivity. Finally, we describe all 4-by-4 sign pattern matrices associated with cycle graphs that require algebraic positivity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-09T10:58:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B35",
      "15B48",
      "05C50"
    ],
    "keywords": [
      "sign pattern matrix",
      "algebraic positivity",
      "cycle graph",
      "real square matrix",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}