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{
    "pk": 64939,
    "title": "Rowmotion on \\(m\\)-Tamari and biCambrian lattices",
    "subtitle": null,
    "abstract": "Thomas and Williams conjectured that rowmotion acting on the rational \\((a,b)\\)-Tamari lattice has order \\(a+b-1\\). We construct an equivariant bijection that proves this conjecture when \\(a\\equiv 1\\pmod b\\); in fact, we determine the entire orbit structure of rowmotion in this case, showing that it exhibits the cyclic sieving phenomenon. We additionally show that the down-degree statistic is homomesic for this action. In a different vein, we consider the action of rowmotion on Barnard and Reading's biCambrian lattices. Settling a different conjecture of Thomas and Williams, we prove that if \\(c\\) is a bipartite Coxeter element of a coincidental-type Coxeter group \\(W\\), then the orbit structure of rowmotion on the \\(c\\)-biCambrian lattice is the same as the orbit structure of rowmotion on the lattice of order ideals of the doubled root poset of type \\(W\\).\n \nMathematics Subject Classifications: 05E18, 06B10, 06D75\n \nKeywords: Rowmotion, \\(m\\)-Tamari lattice, biCambrian lattice, cyclic sieving, homomesy, homometry",
    "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": "Rowmotion"
        },
        {
            "word": "\\(m\\)-Tamari lattice"
        },
        {
            "word": "biCambrian lattice"
        },
        {
            "word": "cyclic sieving"
        },
        {
            "word": "homomesy"
        },
        {
            "word": "homometry"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/5x945586",
    "frozenauthors": [
        {
            "first_name": "Colin",
            "middle_name": "",
            "last_name": "Defant",
            "name_suffix": "",
            "institution": "Department of Mathematics, Harvard University, Cambridge, MA 02139, U.S.A.",
            "department": ""
        },
        {
            "first_name": "James",
            "middle_name": "",
            "last_name": "Lin",
            "name_suffix": "",
            "institution": "Department of Mathematics and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2024-07-01T16:27:52+02:00",
    "date_accepted": "2024-07-01T16:27:52+02:00",
    "date_published": "2025-06-30T09:00:00+02:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64939/galley/49749/download/"
        }
    ]
}