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{
    "pk": 64819,
    "title": "The homogenized Linial arrangement and Genocchi numbers",
    "subtitle": null,
    "abstract": "We study the intersection lattice of a hyperplane arrangement recently introduced by Hetyei who showed that the number of regions of the arrangement is a median Genocchi number. Using a different method, we refine Hetyei's result by providing a combinatorial interpretation of the coefficients of the characteristic polynomial of the intersection lattice of this arrangement. The Genocchi numbers count a class of permutations known as Dumont permutations and the median Genocchi numbers count the derangements in this class. We show that the signless coefficients of the characteristic polynomial count Dumont-like permutations with a given number of cycles. This enables us to derive formulas for the generating function of the characteristic polynomial, which reduce to known formulas for the generating functions of the Genocchi numbers and the median Genocchi numbers. As a byproduct of our work, we obtain new models for the Genocchi and median Genocchi numbers.\n \nMathematics Subject Classifications: 52C35 (Primary), 05A05, 05A15, 05B35, 06A07, 11B68 (Secondary)",
    "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": "Hyperplane arrangement"
        },
        {
            "word": "characteristic polynomial"
        },
        {
            "word": "Genocchi numbers"
        },
        {
            "word": "Dumont permutations"
        },
        {
            "word": "Ferrers graphs"
        },
        {
            "word": "surjective staircases"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/2f1915hz",
    "frozenauthors": [
        {
            "first_name": "Alexander",
            "middle_name": "",
            "last_name": "Lazar",
            "name_suffix": "",
            "institution": "Department of Mathematics, KTH Royal Institute of Technology, Stockholm 114 28, Sweden",
            "department": ""
        },
        {
            "first_name": "Michelle",
            "middle_name": "L.",
            "last_name": "Wachs",
            "name_suffix": "",
            "institution": "Department of Mathematics, University of Miami, Coral Gables, FL 33124, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2022-03-23T19:41:06Z",
    "date_accepted": "2022-03-23T19:41:06Z",
    "date_published": "2022-03-31T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64819/galley/49629/download/"
        }
    ]
}