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{
    "pk": 64851,
    "title": "Multiplication theorems for self-conjugate partitions",
    "subtitle": null,
    "abstract": "In 2011, Han and Ji proved addition-multiplication theorems for integer partitions, from which they derived modular analogues of many classical identities involving hook-length. In the present paper, we prove addition-multiplication theorems for the subset of self-conjugate partitions. Although difficulties arise due to parity questions, we are almost always able to include the BG-rank introduced by Berkovich and Garvan. This gives us as consequences many self-conjugate modular versions of classical hook-lengths identities for partitions. Our tools are mainly based on fine properties of the Littlewood decomposition restricted to self-conjugate partitions.\n \nMathematics Subject Classifications: 05A15, 05A17, 05A19, 05E05, 05E10, 11P81\n \nKeywords: Hook-length formulas, BGP-ranks, Integers partitions, Littlewood decomposition, core partitions",
    "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": "Hook-length formulas"
        },
        {
            "word": "$\\BGP$-ranks"
        },
        {
            "word": "Integers partitions"
        },
        {
            "word": "Littlewood decomposition"
        },
        {
            "word": "core partitions"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/4pd822pc",
    "frozenauthors": [
        {
            "first_name": "David",
            "middle_name": "",
            "last_name": "Wahiche",
            "name_suffix": "",
            "institution": "Institut Camille Jordan, Université Claude Bernard Lyon 1, 69622 Villeurbanne Cedex, France",
            "department": ""
        }
    ],
    "date_submitted": "2022-06-25T20:12:53Z",
    "date_accepted": "2022-06-25T20:12:53Z",
    "date_published": "2022-06-30T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64851/galley/49661/download/"
        }
    ]
}