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{
    "pk": 64960,
    "title": "On linear intervals in the alt \\(\\nu\\)-Tamari lattices",
    "subtitle": null,
    "abstract": "Given a lattice path \\(\\nu\\), the \\(\\nu\\)-Tamari lattice and the \\(\\nu\\)-Dyck lattice are two natural examples of partial order structures on the set of lattice paths that lie weakly above \\(\\nu\\). In this paper, we introduce a more general family of lattices, called alt \\(\\nu\\)-Tamari lattices, which contains these two examples as particular cases. Unexpectedly, we show that all these lattices have the same number of linear intervals.\n \nMathematics Subject Classifications: 06A07, 06B05, 05A19\n \nKeywords: Lattices, intervals, Tamari",
    "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": "Lattices"
        },
        {
            "word": "intervals"
        },
        {
            "word": "Tamari"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/1qb6h2bf",
    "frozenauthors": [
        {
            "first_name": "Cesar",
            "middle_name": "",
            "last_name": "Ceballos",
            "name_suffix": "",
            "institution": "Institute of Geometry, TU Graz, Austria",
            "department": ""
        },
        {
            "first_name": "Clément",
            "middle_name": "",
            "last_name": "Chenevière",
            "name_suffix": "",
            "institution": "Institut de Recherche Mathématique Avancée, Université de Strasbourg, France and Fakultät für Mathematik, Ruhr-Universität Bochum, Germany and Laboratoire Interdisciplinaire des Sciences du Numérique, Université Paris-Saclay, France",
            "department": ""
        }
    ],
    "date_submitted": "2024-09-27T11:41:00+02:00",
    "date_accepted": "2024-09-27T11:41:00+02:00",
    "date_published": "2024-09-30T09:00:00+02:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64960/galley/49770/download/"
        }
    ]
}