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{
    "pk": 65013,
    "title": "Cylindric \\(P\\)-tableaux for \\((\\mathbf{3}+\\mathbf{1})\\) -free posets",
    "subtitle": null,
    "abstract": "Tatsuyki Hikita recently proved the Stanley-Stembridge conjecture, showing that the \\(e\\)-coefficients of the chromatic symmetric function of an incomparability graph of a \\((\\mathbf{3}+\\mathbf{1})\\) -free poset are non-negative. It remains an open problem to find combinatorial interpretations of the \\(e\\)-coefficients. For a \\((\\mathbf{3}+\\mathbf{1})\\)-free \\(P\\), we define a hybrid of \\(P\\)-tableaux and cylindric tableaux called cylindric \\(P\\)-tableaux. The weight generating function of cylindric \\(P\\)-tableaux of shape \\(\\lambda/\\mu/d\\) are shown to be \\(P\\)-analogs of cylindric Schur functions defined by a determinantal formula. We deduce that certain sums of the \\(e\\)-expansion coefficients of the chromatic symmetric function \\(X_{\\operatorname{inc}(P)}\\) are counted by the number of standard cylindric \\(P\\)-tableaux of the appropriate shape. We connect the \\(P\\)-analogs of symmetric functions to a theorem on Hecke algebra immanants due to Clearman-Hyatt-Shelton-Skandera.\n \nMathematics Subject Classifications: 05E05\n \nKeywords: Symmetric Functions, \\(e\\)-Positivity",
    "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": "Symmetric Functions"
        },
        {
            "word": "\\(e\\)-Positivity"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/3577b1dc",
    "frozenauthors": [
        {
            "first_name": "Isaiah",
            "middle_name": "",
            "last_name": "Siegl",
            "name_suffix": "",
            "institution": "Department of Mathematics, University of Washington, Seattle Washington, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2025-09-12T13:33:36Z",
    "date_accepted": "2025-09-12T13:33:36Z",
    "date_published": "2025-09-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/65013/galley/49823/download/"
        }
    ]
}