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{
    "pk": 64957,
    "title": "Promotion permutations for tableaux",
    "subtitle": null,
    "abstract": "<p>We introduce fluctuating tableaux, which subsume many classes of tableaux that have been previously studied, including (generalized) oscillating, vacillating, rational, alternating, standard, and transpose semistandard tableaux. Our main contribution is the introduction of promotion permutations and promotion matrices, which are new even for standard tableaux. We provide characterizations in terms of Bender-Knuth involutions, jeu de taquin, and crystals. We prove key properties in the rectangular case about the behavior of promotion permutations under promotion and evacuation. We also give a full development of the basic combinatorics and representation theory of fluctuating tableaux. Our motivation comes from our companion paper, where we use these results in the development of a new rotation-invariant \\(\\operatorname{SL}_4\\)-web basis. Basis elements are given by certain planar graphs and are constructed so that important algebraic operations can be performed diagrammatically. These planar graphs are indexed by fluctuating tableaux, tableau promotion corresponds to graph rotation, and promotion permutations correspond to key graphical information.</p>\n<p>Mathematics Subject Classifications: 05E10, 05E18</p>\n<p>Keywords: Tableaux, promotion, jeu de taquin, Bender-Knuth involutions, growth diagrams, crystals</p>\n<p>Note: A corrigendum has been added to the published paper</p>",
    "language": null,
    "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": "Tableaux"
        },
        {
            "word": "promotion"
        },
        {
            "word": "jeu de taquin"
        },
        {
            "word": "Bender-Knuth involutions"
        },
        {
            "word": "growth diagrams"
        },
        {
            "word": "crystals"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/1jb964jk",
    "frozenauthors": [
        {
            "first_name": "Christian",
            "middle_name": "",
            "last_name": "Gaetz",
            "name_suffix": "",
            "institution": "Department of Mathematics, University of California, Berkeley, CA, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Oliver",
            "middle_name": "",
            "last_name": "Pechenik",
            "name_suffix": "",
            "institution": "Department of Combinatorics & Optimization, University of Waterloo, ON, Canada",
            "department": ""
        },
        {
            "first_name": "Stephan",
            "middle_name": "",
            "last_name": "Pfannerer",
            "name_suffix": "",
            "institution": "Department of Combinatorics & Optimization, University of Waterloo, ON, Canada",
            "department": ""
        },
        {
            "first_name": "Jessica",
            "middle_name": "",
            "last_name": "Striker",
            "name_suffix": "",
            "institution": "Department of Mathematics, North Dakota State University, Fargo, ND, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Joshua",
            "middle_name": "P.",
            "last_name": "Swanson",
            "name_suffix": "",
            "institution": "Department of Mathematics, University of Southern California, Los Angeles, CA, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2024-09-27T11:12:22+02:00",
    "date_accepted": "2024-09-27T11:12:22+02:00",
    "date_published": "2024-09-30T09:00:00+02:00",
    "render_galley": null,
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            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64957/galley/49767/download/"
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}