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{
    "pk": 64920,
    "title": "Schubert matroids, Delannoy paths, and Speyer's invariant",
    "subtitle": null,
    "abstract": "We provide a combinatorial way of computing Speyer's \\(g\\)-polynomial on arbitrary Schubert matroids via the enumeration of certain Delannoy paths. We define a new statistic of a basis in a matroid, and express the \\(g\\)-polynomial of a Schubert matroid in terms of it and internal and external activities. Some surprising positivity properties of the \\(g\\)-polynomial of Schubert matroids are deduced from our expression. Finally, we combine our formulas with a fundamental result of Derksen and Fink to provide an algorithm for computing the \\(g\\)-polynomial of an arbitrary matroid.\n \nMathematics Subject Classifications: 05B35, 52B40, 14T15\n \nKeywords: Schubert matroids, \\(g\\)-polynomial, matroid polytopes, series-parallel matroids, lattice path enumeration",
    "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": "Schubert matroids"
        },
        {
            "word": "\\(g\\)-polynomial"
        },
        {
            "word": "matroid polytopes"
        },
        {
            "word": "series-parallel matroids"
        },
        {
            "word": "lattice path enumeration"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/4n0207rm",
    "frozenauthors": [
        {
            "first_name": "Luis",
            "middle_name": "",
            "last_name": "Ferroni",
            "name_suffix": "",
            "institution": "KTH Royal Institute of Technology, Stockholm, Sweden",
            "department": ""
        }
    ],
    "date_submitted": "2023-12-22T14:16:35Z",
    "date_accepted": "2023-12-22T14:16:35Z",
    "date_published": "2023-12-22T08:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64920/galley/49730/download/"
        }
    ]
}