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{
    "pk": 64936,
    "title": "On quasi-polynomials counting planar tight maps",
    "subtitle": null,
    "abstract": "A tight map is a map with some of its vertices marked, such that every vertex of degree \\(1\\) is marked. We give an explicit formula for the number \\(N_{0,n}(d_1,\\ldots,d_n)\\) of planar tight maps with \\(n\\) labeled faces of prescribed degrees \\(d_1,\\ldots,d_n\\), where a marked vertex is seen as a face of degree \\(0\\). It is a quasi-polynomial in \\((d_1,\\ldots,d_n)\\), as shown previously by Norbury. Our derivation is bijective and based on the slice decomposition of planar maps. In the non-bipartite case, we also rely on enumeration results for two-type forests. We discuss the connection with the enumeration of non necessarily tight maps. In particular, we provide a generalization of Tutte's classical slicings formula to all non-bipartite maps.\n \nMathematics Subject Classifications: 05A15, 05A19\n \nKeywords: Planar maps, bijective enumeration, slice decomposition",
    "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": "Planar maps"
        },
        {
            "word": "bijective enumeration"
        },
        {
            "word": "slice decomposition"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/9h946160",
    "frozenauthors": [
        {
            "first_name": "Jérémie",
            "middle_name": "",
            "last_name": "Bouttier",
            "name_suffix": "",
            "institution": "Sorbonne Université and Université Paris Cité, CNRS, IMJ-PRG, F-75005 Paris, France -- Université Paris-Saclay, CNRS, CEA, Institut de physique théorique, 91191, Gif-sur-Yvette, France",
            "department": ""
        },
        {
            "first_name": "Emmanuel",
            "middle_name": "",
            "last_name": "Guitter",
            "name_suffix": "",
            "institution": "Université Paris-Saclay, CNRS, CEA, Institut de physique théorique, 91191, Gif-sur-Yvette, France",
            "department": ""
        },
        {
            "first_name": "Grégory",
            "middle_name": "",
            "last_name": "Miermont",
            "name_suffix": "",
            "institution": "ENS de Lyon, UMPA, CNRS UMR 5669, 46 allée d’Italie, 69364 Lyon Cedex 07, France",
            "department": ""
        }
    ],
    "date_submitted": "2024-07-01T16:17:38+02:00",
    "date_accepted": "2024-07-01T16:17:38+02:00",
    "date_published": "2024-06-30T09:00:00+02:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64936/galley/49746/download/"
        }
    ]
}