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{
    "pk": 64994,
    "title": "The cyclicity rank of empty lattice simplices",
    "subtitle": null,
    "abstract": "We are interested in algebraic properties of empty lattice simplices \\(\\Delta\\), that is, \\(d\\)-dimensional lattice polytopes containing exactly \\(d+1\\) points of the integer lattice \\(\\mathbb{Z}^d\\). The cyclicity rank of \\(\\Delta\\) is the minimal number of cyclic subgroups that the quotient group of \\(\\Delta\\) splits into. It is known that up to dimension \\(d \\leq 4\\), every empty lattice \\(d\\)-simplex is cyclic, meaning that its cyclicity rank is at most \\(1\\). We determine the maximal possible cyclicity rank of an empty lattice \\(d\\)-simplex for dimensions \\(d \\leq 8\\), and determine the asymptotics of this number up to a logarithmic term.\n \nMathematics Subject Classifications: 52B20, 11H06, 14E30\n \nKeywords: Empty lattice simplices, quotient groups, Hermite normal forms",
    "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": "Empty lattice simplices"
        },
        {
            "word": "quotient groups"
        },
        {
            "word": "Hermite normal forms"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/49g6g85x",
    "frozenauthors": [
        {
            "first_name": "Lukas",
            "middle_name": "",
            "last_name": "Abend",
            "name_suffix": "",
            "institution": "Institute of Mathematics, University of Rostock, Germany",
            "department": ""
        },
        {
            "first_name": "Matthias",
            "middle_name": "",
            "last_name": "Schymura",
            "name_suffix": "",
            "institution": "Institute of Mathematics, University of Rostock, Germany",
            "department": ""
        }
    ],
    "date_submitted": "2025-07-15T15:37:45Z",
    "date_accepted": "2025-07-15T15:37:45Z",
    "date_published": "2025-07-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64994/galley/49804/download/"
        }
    ]
}