{
  "id": "2408.12386",
  "version": "v1",
  "published": "2024-08-22T13:27:22.000Z",
  "updated": "2024-08-22T13:27:22.000Z",
  "title": "Preservation of inequalities under Hadamard products",
  "authors": [
    "Petter Brändén",
    "Luis Ferroni",
    "Katharina Jochemko"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Wagner (1992) proved that the Hadamard product of two P\\'olya frequency sequences that are interpolated by polynomials is again a P\\'olya frequency sequence. We study the preservation under Hadamard products of related properties of significance in combinatorics. In particular, we show that ultra log-concavity, $\\gamma$-positivity, and interlacing symmetric decompositions are preserved. Furthermore, we disprove a conjecture by Fischer and Kubitzke (2014) concerning the real-rootedness of Hadamard powers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-22T13:27:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hadamard product",
      "polya frequency sequence",
      "preservation",
      "inequalities",
      "ultra log-concavity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}