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{
    "pk": 64903,
    "title": "Homomesy via toggleability statistics",
    "subtitle": null,
    "abstract": "The rowmotion operator acting on the set of order ideals of a finite poset has been the focus of a significant amount of recent research. One of the major goals has been to exhibit homomesies: statistics that have the same average along every orbit of the action. We systematize a technique for proving that various statistics of interest are homomesic by writing these statistics as linear combinations of \"toggleability statistics\" (originally introduced by Striker) plus a constant. We show that this technique recaptures most of the known homomesies for the posets on which rowmotion has been most studied. We also show that the technique continues to work in modified contexts. For instance, this technique also yields homomesies for the piecewise-linear and birational extensions of rowmotion; furthermore, we introduce a \\(q\\)-analogue of rowmotion and show that the technique yields homomesies for \"\\(q\\)-rowmotion\" as well.\n \nMathematics Subject Classifications: 06A07, 05E18, 05A30, 52B05\n \nKeywords: Homomesy, rowmotion, toggling, piecewise-linear & birational lift, \\(q\\)-analogue",
    "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": "Homomesy"
        },
        {
            "word": "rowmotion"
        },
        {
            "word": "toggling"
        },
        {
            "word": "piecewise-linear &amp"
        },
        {
            "word": "birational lift"
        },
        {
            "word": "\\(q\\)-analogue"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/53j5m46g",
    "frozenauthors": [
        {
            "first_name": "Colin",
            "middle_name": "",
            "last_name": "Defant",
            "name_suffix": "",
            "institution": "Department of Mathematics, Harvard University, Cambridge, MA, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Sam",
            "middle_name": "",
            "last_name": "Hopkins",
            "name_suffix": "",
            "institution": "Department of Mathematics, Howard University, Washington, DC, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Svetlana",
            "middle_name": "",
            "last_name": "Poznanović",
            "name_suffix": "",
            "institution": "School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC, U.S.A.",
            "department": ""
        },
        {
            "first_name": "James",
            "middle_name": "",
            "last_name": "Propp",
            "name_suffix": "",
            "institution": "Department of Mathematics and Statistics, University of Massachusetts Lowell, Lowell, MA, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2023-09-14T08:15:32Z",
    "date_accepted": "2023-09-14T08:15:32Z",
    "date_published": "2023-09-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64903/galley/49713/download/"
        }
    ]
}