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{
    "pk": 64999,
    "title": "A combinatorial skewing formula for the Rise Delta Theorem",
    "subtitle": null,
    "abstract": "We prove that the symmetric function \\(\\Delta'_{e_{k-1}}e_n\\) appearing in the Delta Conjecture can be obtained from the symmetric function in the Rectangular Shuffle Theorem by applying a Schur skewing operator. This generalizes a formula by the first and third authors for the Delta Conjecture at \\(t=0\\), and follows from work of Blasiak, Haiman, Morse, Pun, and Seelinger. Our main result is that we also provide a purely combinatorial proof of this skewing identity, giving a new proof of the Rise Delta Theorem from the Rectangular Shuffle Theorem.\n \nMathematics Subject Classifications: 05E05\n \nKeywords: Delta conjecture, parking functions, sign reversing involutions, skewing formula, Rectangular shuffle theorem, dinv, symmetric functions",
    "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": "Delta conjecture"
        },
        {
            "word": "parking functions"
        },
        {
            "word": "sign reversing involutions"
        },
        {
            "word": "skewing formula"
        },
        {
            "word": "Rectangular shuffle theorem"
        },
        {
            "word": "dinv"
        },
        {
            "word": "symmetric functions"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/3bp930rf",
    "frozenauthors": [
        {
            "first_name": "Maria",
            "middle_name": "",
            "last_name": "Gillespie",
            "name_suffix": "",
            "institution": "Department of Mathematics, Colorado State University, Fort Collins, CO, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Eugene",
            "middle_name": "",
            "last_name": "Gorsky",
            "name_suffix": "",
            "institution": "Department of Mathematics, University of California Davis, One Shields Ave, Davis CA, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Sean",
            "middle_name": "",
            "last_name": "Griffin",
            "name_suffix": "",
            "institution": "Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria",
            "department": ""
        }
    ],
    "date_submitted": "2025-09-12T10:13:08Z",
    "date_accepted": "2025-09-12T10:13:08Z",
    "date_published": "2025-09-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64999/galley/49809/download/"
        }
    ]
}