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{
    "pk": 64886,
    "title": "Bar-and-joint rigidity on the moment curve coincides with cofactor rigidity on a conic",
    "subtitle": null,
    "abstract": "We show that, for points along the moment curve, the bar-and-joint rigidity matroid and the hyperconnectivity matroid coincide, and that both coincide with the \\(C^{d-2}_{d-1}\\)-cofactor rigidity of points along any (non-degenerate) conic in the plane. For hyperconnectivity in dimension two, having the points in the moment curve is no loss of generality. We also show that, restricted to bipartite graphs, the bar-and-joint rigidity matroid is freer than the hyperconnectivity matroid.\n \nMathematics Subject Classifications: 52C25, 52B40\n \nKeywords: Rigidity, hyperconnectivity, moment curve, cofactor rigidity",
    "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": "Rigidity"
        },
        {
            "word": "hyperconnectivity"
        },
        {
            "word": "moment curve"
        },
        {
            "word": "cofactor rigidity"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/7n514431",
    "frozenauthors": [
        {
            "first_name": "Luis",
            "middle_name": "",
            "last_name": "Crespo Ruiz",
            "name_suffix": "",
            "institution": "Department of Mathematics, Statistics and Computing, Universidad de Cantabria, Santander, Spain",
            "department": ""
        },
        {
            "first_name": "Francisco",
            "middle_name": "",
            "last_name": "Santos",
            "name_suffix": "",
            "institution": "Department of Mathematics, Statistics and Computing, Universidad de Cantabria, Santander, Spain",
            "department": ""
        }
    ],
    "date_submitted": "2023-03-14T16:42:52Z",
    "date_accepted": "2023-03-14T16:42:52Z",
    "date_published": "2023-03-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64886/galley/49696/download/"
        }
    ]
}