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{
    "pk": 65034,
    "title": "Representability of the direct sum of uniform \\(q\\)-matroids",
    "subtitle": null,
    "abstract": "There are many similarities between the theories of matroids and \\(q\\)-matroids. However, when dealing with the direct sum of \\(q\\)-matroids many differences arise. Most notably, it has recently been shown that the direct sum of representable \\(q\\)-matroids is not necessarily representable. In this work, we focus on the direct sum of uniform \\(q\\)-matroids. Using algebraic and geometric tools, together with the notion of cyclic flats of \\(q\\)-matroids, we show that this is always representable, by providing a representation over a sufficiently large field.\n \nMathematics Subject Classifications: 05B35, 94B05, 51E20\n \nKeywords: \\(q\\)-matroids, representability, evasive subspaces, rank-metric codes, linear sets",
    "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": "\\(q\\)-matroids"
        },
        {
            "word": "representability"
        },
        {
            "word": "evasive subspaces"
        },
        {
            "word": "rank-metric codes"
        },
        {
            "word": "linear sets"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/8s66b3x9",
    "frozenauthors": [
        {
            "first_name": "Gianira",
            "middle_name": "N.",
            "last_name": "Alfarano",
            "name_suffix": "",
            "institution": "Université de Rennes, IRMAR - UMR 6625, Rennes Cedex, France -- School of Mathematics and Statistics, University College Dublin, Ireland -- Department of Mathematics and Data Science, Vrije Universiteit Brussel, Belgium",
            "department": ""
        },
        {
            "first_name": "Relinde",
            "middle_name": "",
            "last_name": "Jurrius",
            "name_suffix": "",
            "institution": "Faculty of Military Sciences, Netherlands Defence Academy, the Netherlands",
            "department": ""
        },
        {
            "first_name": "Alessandro",
            "middle_name": "",
            "last_name": "Neri",
            "name_suffix": "",
            "institution": "Department of Mathematics and Applications \"R. Caccioppoli\", University of Naples Federico II, Napoli, Italy -- Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium",
            "department": ""
        },
        {
            "first_name": "Ferdinando",
            "middle_name": "",
            "last_name": "Zullo",
            "name_suffix": "",
            "institution": "Department of Mathematics and Physics, University of Campania \"Luigi Vanvitelli\", Caserta, Italy",
            "department": ""
        }
    ],
    "date_submitted": "2026-04-20T12:09:39-07:00",
    "date_accepted": "2026-04-20T12:09:39-07:00",
    "date_published": "2026-04-20T00:00:00-07:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/65034/galley/49844/download/"
        }
    ]
}