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{
    "pk": 64834,
    "title": "No extremal square-free words over large alphabets",
    "subtitle": null,
    "abstract": "A word is square-free if it does not contain any square (a word of the form $XX$), and is extremal square-free if it cannot be extended to a new square-free word by inserting a single letter at any position. Grytczuk, Kordulewski, and Niewiadomski proved that there exist infinitely many ternary extremal square-free words. We establish that there are no extremal square-free words over any alphabet of size at least $17$.\n \nMathematics Subject Classifications: 05A05, 05D10, 68R15",
    "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": "Combinatorics on words"
        },
        {
            "word": "square-free words"
        },
        {
            "word": "extremal words"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/23b1m1rf",
    "frozenauthors": [
        {
            "first_name": "Letong",
            "middle_name": "",
            "last_name": "Hong",
            "name_suffix": "",
            "institution": "Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02142, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Shengtong",
            "middle_name": "",
            "last_name": "Zhang",
            "name_suffix": "",
            "institution": "Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02142, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2022-03-23T21:09:11Z",
    "date_accepted": "2022-03-23T21:09:11Z",
    "date_published": "2022-03-31T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64834/galley/49644/download/"
        }
    ]
}