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{
    "pk": 64887,
    "title": "Von Staudt constructions for skew-linear and multilinear matroids",
    "subtitle": null,
    "abstract": "This paper compares skew-linear and multilinear matroid representations. These are matroids that are representable over division rings and (roughly speaking) invertible matrices, respectively. The main tool is the von Staudt construction, by which we translate our problems to algebra. After giving an exposition of a simple variant of the von Staudt construction we present the following results:\nUndecidability of several matroid representation problems over division rings.\n \nAn example of a matroid with an infinite multilinear characteristic set, but which is not multilinear in characteristic \\(0\\).\n \nAn example of a skew-linear matroid that is not multilinear.\n \n \n \nMathematics Subject Classifications: 05B35, 52B40, 14N20, 52C35, 20F10, 03D40\n \nKeywords: Matroids, division ring representations, subspace arrangements, \\(c\\)-arrange\\-ments, multilinear matroids, von Staudt constructions, word problem, Weyl algebra,  Baumslag-Solitar group",
    "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": "Matroids"
        },
        {
            "word": "division ring representations"
        },
        {
            "word": "subspace arrangements"
        },
        {
            "word": "\\(c\\)-arrange\\-ments"
        },
        {
            "word": "multilinear matroids"
        },
        {
            "word": "von Staudt constructions"
        },
        {
            "word": "word problem"
        },
        {
            "word": "Weyl algebra"
        },
        {
            "word": "Baumslag-Solitar group"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/01q1x044",
    "frozenauthors": [
        {
            "first_name": "Lukas",
            "middle_name": "",
            "last_name": "Kühne",
            "name_suffix": "",
            "institution": "Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany",
            "department": ""
        },
        {
            "first_name": "Rudi",
            "middle_name": "",
            "last_name": "Pendavingh",
            "name_suffix": "",
            "institution": "Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands",
            "department": ""
        },
        {
            "first_name": "Geva",
            "middle_name": "",
            "last_name": "Yashfe",
            "name_suffix": "",
            "institution": "Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Giv’at Ram, 9190401 Jerusalem, Israel",
            "department": ""
        }
    ],
    "date_submitted": "2023-03-14T16:45:32Z",
    "date_accepted": "2023-03-14T16:45:32Z",
    "date_published": "2023-03-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64887/galley/49697/download/"
        }
    ]
}