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{
    "pk": 64979,
    "title": "Systems of Discrete Differential Equations, Constructive Algebraicity of the Solutions",
    "subtitle": null,
    "abstract": "In this article, we study systems of \\(n\\geq 1\\), not necessarily linear, discrete differential equations (DDEs) of order \\(k\\geq 1\\) with one catalytic variable. We provide a constructive and elementary proof of algebraicity of the solutions of such equations. This part of the present article can be seen as a generalization of the pioneering work by Bousquet-Mélou and Jehanne (2006) who settled down the case \\(n=1\\). Moreover, we obtain effective bounds for the algebraicity degrees of the solutions and provide an algorithm for computing annihilating polynomials of the algebraic series. Finally, we compare three different strategies for solving systems of DDEs in view of practical applications.\n \nMathematics Subject Classifications: 05A99, 13A99, 14R15\n \nKeywords: Catalytic variable, algebraic series, formal power series, discrete differential equations, polynomial systems",
    "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": "Catalytic variable"
        },
        {
            "word": "algebraic series"
        },
        {
            "word": "formal power series"
        },
        {
            "word": "discrete differential equations"
        },
        {
            "word": "polynomial systems"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/58x5z12z",
    "frozenauthors": [
        {
            "first_name": "Hadrien",
            "middle_name": "",
            "last_name": "Notarantonio",
            "name_suffix": "",
            "institution": "IRIF, CNRS UMR 8243, Université Paris Cité, France",
            "department": ""
        },
        {
            "first_name": "Sergey",
            "middle_name": "",
            "last_name": "Yurkevich",
            "name_suffix": "",
            "institution": "A&R TECH, Dietz-von-Weidenberg-Gasse 2, 1210 Vienna, Austria",
            "department": ""
        }
    ],
    "date_submitted": "2025-07-15T14:53:35Z",
    "date_accepted": "2025-07-15T14:53:35Z",
    "date_published": "2025-07-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64979/galley/49789/download/"
        }
    ]
}