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{
    "pk": 64816,
    "title": "Hidden automatic sequences",
    "subtitle": null,
    "abstract": "An automatic sequence is a letter-to-letter coding of a fixed point of a uniform morphism. More generally, morphic sequences are letter-to-letter codings of fixed points of arbitrary morphisms. There are many examples where an, a priori, morphic sequence with a non-uniform morphism happens to be an automatic sequence. An example is the Lysënok morphism $a \\to aca$, $b \\to d$, $c \\to b$, $d \\to c$, the fixed point of which is also a $2$-automatic sequence. Such an identification is useful for describing the dynamical systems generated by the fixed point. We give several ways to uncover such hidden automatic sequences, and present many examples. We focus in particular on morphisms associated with Grigorchuk groups.\nKeywords: Morphic sequences, automatic sequences, Grigorchuk groups.\nMathematics Subject Classifications: 11B85, 68R15, 37B10",
    "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": [],
    "section": "Expository Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/75c3n0bc",
    "frozenauthors": [
        {
            "first_name": "Jean-Paul",
            "middle_name": "",
            "last_name": "Allouche",
            "name_suffix": "",
            "institution": "CNRS, IMJ-PRG, UPMC, 4 Place Jussieu, F-75252 Paris Cedex 05, France",
            "department": ""
        },
        {
            "first_name": "Michel",
            "middle_name": "",
            "last_name": "Dekking",
            "name_suffix": "",
            "institution": "Delft University of Technology, Faculty EEMCS, P.O. Box 5031, 2600 GA Delft, The Netherlands",
            "department": ""
        },
        {
            "first_name": "Martine",
            "middle_name": "",
            "last_name": "Queffélec",
            "name_suffix": "",
            "institution": "Université Lille 1, UMR 8524, F-59655 Villeneuve d'Ascq Cedex, France",
            "department": ""
        }
    ],
    "date_submitted": "2021-11-12T22:09:09Z",
    "date_accepted": "2021-11-12T22:09:09Z",
    "date_published": "2021-12-15T08:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64816/galley/49626/download/"
        }
    ]
}