{
  "id": "2410.07581",
  "version": "v1",
  "published": "2024-10-10T03:29:56.000Z",
  "updated": "2024-10-10T03:29:56.000Z",
  "title": "Clocks are $e$-positive",
  "authors": [
    "L. Chen",
    "Y. T. He",
    "David G. L. Wang"
  ],
  "comment": "15 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Along with his confirmation of the $e$-positivity of all cycle-chord graphs $\\theta_{ab1}$, the third author conjectured the $e$-positivity of all theta graphs $\\theta_{abc}$. In this paper, we establish the $e$-positivity of all clock graphs $\\theta_{ab2}$ by using the composition method. The key idea is to investigate the fibers of certain partial reversal transformation on compositions with all parts at least $2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-10T03:29:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05"
    ],
    "keywords": [
      "positivity",
      "partial reversal transformation",
      "clock graphs",
      "third author",
      "composition method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}