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{
    "pk": 65026,
    "title": "The foundation of generalized parallel connections, 2-sums, and segment-cosegment exchanges of matroids",
    "subtitle": null,
    "abstract": "We show that, under suitable hypotheses, the foundation of a generalized parallel connection of matroids is the relative tensor product of the foundations. Using this result, we show that the foundation of a 2-sum of matroids is the absolute tensor product of the foundations, and that the foundation of a matroid is invariant under segment-cosegment exchange.\n \nMathematics Subject Classifications: 05B35, 20Axx\n \nKeywords: Matroids, pastures, foundations, generalized parallel connection, 2-sum,  segment-cosegment exchange",
    "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": "pastures"
        },
        {
            "word": "foundations"
        },
        {
            "word": "generalized parallel connection"
        },
        {
            "word": "2-sum"
        },
        {
            "word": "segment-cosegment exchange"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/2zm4n53x",
    "frozenauthors": [
        {
            "first_name": "Matthew",
            "middle_name": "",
            "last_name": "Baker",
            "name_suffix": "",
            "institution": "School of Mathematics, Georgia Institute of Technology, Atlanta, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Oliver",
            "middle_name": "",
            "last_name": "Lorscheid",
            "name_suffix": "",
            "institution": "Mathematics Department, University of Groningen, Groningen, Netherlands",
            "department": ""
        },
        {
            "first_name": "Zach",
            "middle_name": "",
            "last_name": "Walsh",
            "name_suffix": "",
            "institution": "Department of Mathematics and Statistics, Auburn University, Auburn, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Tianyi",
            "middle_name": "",
            "last_name": "Zhang",
            "name_suffix": "",
            "institution": "School of Mathematics, Georgia Institute of Technology, Atlanta, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2026-02-02T10:07:12Z",
    "date_accepted": "2026-02-02T10:07:12Z",
    "date_published": "2025-12-20T08:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/65026/galley/49836/download/"
        }
    ]
}