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{
    "pk": 64984,
    "title": "Upho lattices I: examples and non-examples of cores",
    "subtitle": null,
    "abstract": "A poset is called upper homogeneous, or \"upho,\" if every principal order filter of the poset is isomorphic to the whole poset. We study (finite type \\(\\mathbb{N}\\)-graded) upho lattices, with an eye towards their classification. Any upho lattice has associated to it a finite graded lattice called its core, which determines its rank generating function. We investigate which finite graded lattices arise as cores of upho lattices, providing both positive and negative results. On the one hand, we show that many well-studied finite lattices do arise as cores, and we present combinatorial and algebraic constructions of the upho lattices into which they embed. On the other hand, we show there are obstructions which prevent many finite lattices from being cores.\n \nMathematics Subject Classifications: 06A07, 05B35, 06C10, 20M32\n \nKeywords: Upho posets, rank generating functions, characteristic polynomials, geometric lattices, supersolvable lattices, Dowling lattices, Garside monoids",
    "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": "Upho posets"
        },
        {
            "word": "rank generating functions"
        },
        {
            "word": "characteristic polynomials"
        },
        {
            "word": "geometric lattices"
        },
        {
            "word": "supersolvable lattices"
        },
        {
            "word": "Dowling lattices"
        },
        {
            "word": "Garside monoids"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/2w34138p",
    "frozenauthors": [
        {
            "first_name": "Sam",
            "middle_name": "",
            "last_name": "Hopkins",
            "name_suffix": "",
            "institution": "Department of Mathematics, Howard University, Washington, DC, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2025-07-15T20:08:46+05:00",
    "date_accepted": "2025-07-15T20:08:46+05:00",
    "date_published": "2025-07-15T12:00:00+05:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64984/galley/49794/download/"
        }
    ]
}