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{
    "pk": 65006,
    "title": "An explicit condition for boundedly supermultiplicative subshifts",
    "subtitle": null,
    "abstract": "We study some properties of the growth rate of \\(\\mathcal{L}(\\mathcal{A},\\mathcal{F})\\), that is, the language of words over the alphabet \\(\\mathcal{A}\\) avoiding the set of forbidden factors \\(\\mathcal{F}\\). We first provide a sufficient condition on \\(\\mathcal{F}\\) and \\(\\mathcal{A}\\) for the growth of \\(\\mathcal{L}(\\mathcal{A},\\mathcal{F})\\) to be boundedly supermultiplicative. That is, there exist constants \\(C›0\\) and \\(\\alpha\\ge0\\), such that for all \\(n\\), the number of words of length \\(n\\) in \\(\\mathcal{L}(\\mathcal{A},\\mathcal{F})\\) is between \\(\\alpha^n\\) and \\(C\\alpha^n\\). In some settings, our condition provides a way to compute \\(C\\), which implies that \\(\\alpha\\), the growth rate of the language, is also computable whenever our condition holds.\nWe also apply our technique to the specific setting of power-free words where the argument can be slightly refined to provide better bounds. Finally, we apply a similar idea to \\(\\mathcal{F}\\)-free circular words and in particular we make progress toward a conjecture of Shur about the number of square-free circular words.\n \nMathematics Subject Classifications: 68R15\n \nKeywords: Subshift, supermultiplicativity, growth of languages,  circular word",
    "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": "Subshift"
        },
        {
            "word": "supermultiplicativity"
        },
        {
            "word": "growth of languages"
        },
        {
            "word": "circular word"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/563364s6",
    "frozenauthors": [
        {
            "first_name": "Vuong",
            "middle_name": "",
            "last_name": "Bui",
            "name_suffix": "",
            "institution": "Swinburne Vietnam, FPT University, Hanoi, 80 Duy Tan Street, Hanoi 100000, Vietnam",
            "department": ""
        },
        {
            "first_name": "Matthieu",
            "middle_name": "",
            "last_name": "Rosenfeld",
            "name_suffix": "",
            "institution": "LIRMM, Université de Montpellier, CNRS, 161 Rue Ada, 34095 Montpellier, France",
            "department": ""
        }
    ],
    "date_submitted": "2025-09-12T12:07:21Z",
    "date_accepted": "2025-09-12T12:07:21Z",
    "date_published": "2025-09-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/65006/galley/49816/download/"
        }
    ]
}