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{
    "pk": 64810,
    "title": "A combinatorial Schur expansion of triangle-free horizontal-strip LLT polynomials",
    "subtitle": null,
    "abstract": "In recent years, Alexandersson and others proved combinatorial formulas for the Schur function expansion of the horizontal-strip LLT polynomial $G_{\\boldsymbol\\lambda}(\\boldsymbol x;q)$ in some special cases. We associate a weighted graph $\\Pi$ to $\\boldsymbol\\lambda$ and we use it to express a linear relation among LLT polynomials. We apply this relation to prove an explicit combinatorial Schur-positive expansion of $G_{\\boldsymbol\\lambda}(\\boldsymbol x;q)$ whenever $\\Pi$ is triangle-free. We also prove that the largest power of $q$ in the LLT polynomial is the total edge weight of our graph.\nKeywords: Charge, chromatic symmetric function, cocharge, Hall--Littlewood polynomial, jeu de taquin, LLT polynomial, interval graph, Schur function, Schur-positive, symmetric function.\nMathematics Subject Classifications: 05E05, 05E10, 05C15",
    "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": [],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/88f1079r",
    "frozenauthors": [
        {
            "first_name": "Foster",
            "middle_name": "",
            "last_name": "Tom",
            "name_suffix": "",
            "institution": "Department of Mathematics, University of California, Berkeley, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2021-11-12T21:39:26Z",
    "date_accepted": "2021-11-12T21:39:26Z",
    "date_published": "2021-12-15T08:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64810/galley/49620/download/"
        }
    ]
}