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{
    "pk": 64854,
    "title": "A refinement of the Murnaghan-Nakayama rule by descents for border strip tableaux",
    "subtitle": null,
    "abstract": "Lusztig's fake degree is the generating polynomial for the major index of standard Young tableaux of a given shape. Results of Springer (1974) and James & Kerber (1984) imply that, mysteriously, its evaluation at a $k$-th primitive root of unity yields the number of border strip tableaux with all strips of size $k$, up to sign. This is essentially the special case of the Murnaghan-Nakayama rule for evaluating an irreducible character of the symmetric group at a rectangular partition.  We refine this result to standard Young tableaux and border strip tableaux with a given number of descents. To do so, we introduce a new statistic for border strip tableaux, extending the classical definition of descents in standard Young tableaux. Curiously, it turns out that our new statistic is very closely related to a descent set for tuples of standard Young tableaux appearing in the quasisymmetric expansion of LLT polynomials given by Haglund, Haiman and Loehr (2005).\n \nMathematics Subject Classifications: 05A19, 05E10\n \nKeywords: Border strip tableaux, descents, Murnaghan-Nakayama rule, fake degree",
    "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": "Border strip tableaux"
        },
        {
            "word": "descents"
        },
        {
            "word": "Murnaghan-Nakayama rule"
        },
        {
            "word": "fake degree"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/9cs438vb",
    "frozenauthors": [
        {
            "first_name": "Stephan",
            "middle_name": "",
            "last_name": "Pfannerer",
            "name_suffix": "",
            "institution": "Institut für Diskrete Mathematik und Geometrie, TU Wien, Austria",
            "department": ""
        }
    ],
    "date_submitted": "2022-06-25T20:32:04Z",
    "date_accepted": "2022-06-25T20:32:04Z",
    "date_published": "2022-06-30T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64854/galley/49664/download/"
        }
    ]
}