Article Instance

HTTP 200 OK
Allow: GET
Content-Type: application/json
Vary: Accept

{
    "pk": 64975,
    "title": "Eulerian polynomials for digraphs",
    "subtitle": null,
    "abstract": "Given an \\(n\\)-vertex digraph \\(D\\) and a labeling \\(\\sigma:V(D)\\to [n]\\), we say that an arc \\(u\\to v\\) of \\(D\\) is a descent of \\(\\sigma\\) if \\(\\sigma(u)›\\sigma(v)\\). Foata and Zeilberger introduced a generating function \\(A_D(t)\\) for labelings of \\(D\\) weighted by descents, which simultaneously generalizes both Eulerian polynomials and Mahonian polynomials. Motivated in part by work of Kalai, we prove three results related to \\(-1\\) evaluations of \\(A_D(t)\\): we give combinatorial interpretations of \\(|A_D(-1)|\\) for a large class of digraphs (such as digraphs whose underlying graph is bipartite), we determine the maximum and minimum possible values of \\(|A_D(-1)|\\) obtained by directed trees, and we obtain bounds on the mulitiplicity of \\(-1\\) as a root of \\(A_D(t)\\).\n \nMathematics Subject Classifications: 05C20, 05A15\n \nKeywords: Eulerian polynomials, alternating permutations, combinatorial reciprocity",
    "language": "en",
    "license": {
        "name": "Creative Commons Attribution 4.0",
        "short_name": "CC BY 4.0",
        "text": "Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.",
        "url": "https://creativecommons.org/licenses/by/4.0"
    },
    "keywords": [
        {
            "word": "Eulerian polynomials"
        },
        {
            "word": "alternating permutations"
        },
        {
            "word": "combinatorial reciprocity"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/7ph7d2pk",
    "frozenauthors": [
        {
            "first_name": "Kyle",
            "middle_name": "",
            "last_name": "Celano",
            "name_suffix": "",
            "institution": "Department of Mathematics, Wake Forest University, Winston Salem, North Carolina, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Nicholas",
            "middle_name": "",
            "last_name": "Sieger",
            "name_suffix": "",
            "institution": "Department of Mathematics, Iowa State University, Ames, Iowa, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Sam",
            "middle_name": "",
            "last_name": "Spiro",
            "name_suffix": "",
            "institution": "Department of Mathematics, Rutgers University, Piscataway, New Jersey, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2025-03-14T17:04:02Z",
    "date_accepted": "2025-03-14T17:04:02Z",
    "date_published": "2025-03-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64975/galley/49785/download/"
        }
    ]
}