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{
    "pk": 65046,
    "title": "Uncountably many enumerations of well-quasi-ordered permutation classes",
    "subtitle": null,
    "abstract": "We construct an uncountable family of well-quasi-ordered permutation classes, each with a distinct enumeration sequence. This disproves a conjecture that all well-quasi-ordered permutation classes have algebraic generating functions, and in fact shows that many such classes lack D-finite or D-algebraic generating functions. Our construction is based on an uncountably large collection of factor-closed, well-quasi-ordered binary languages due to Pouzet.\n \nMathematics Subject Classifications: 05A05, 05A15, 06A07\n \nKeywords: Generating functions, permutation classes, well-quasi-order",
    "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": "Generating functions"
        },
        {
            "word": "permutation classes"
        },
        {
            "word": "well-quasi-order"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/4kh7t5t9",
    "frozenauthors": [
        {
            "first_name": "Robert",
            "middle_name": "",
            "last_name": "Brignall",
            "name_suffix": "",
            "institution": "School of Mathematics and Statistics, The Open University, Milton Keynes, England, U.K.",
            "department": ""
        },
        {
            "first_name": "Vincent",
            "middle_name": "",
            "last_name": "Vatter",
            "name_suffix": "",
            "institution": "Department of Mathematics, University of Florida, Gainesville, Florida, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2026-04-20T12:57:37-07:00",
    "date_accepted": "2026-04-20T12:57:37-07:00",
    "date_published": "2026-04-20T00:00:00-07:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/65046/galley/49856/download/"
        }
    ]
}