Article Instance

HTTP 200 OK
Allow: GET
Content-Type: application/json
Vary: Accept

{
    "pk": 64987,
    "title": "Combinatorics of \\(m = 1\\) grasstopes",
    "subtitle": null,
    "abstract": "A Grasstope is the image of the totally nonnegative Grassmannian \\(\\operatorname{Gr}_{\\geq 0}(k,n)\\) under a linear map \\(\\operatorname{Gr}(k,n)\\dashrightarrow \\operatorname{Gr}(k,k+m)\\). This is a generalization of the amplituhedron, a geometric object of great importance to calculating scattering amplitudes in physics. The amplituhedron is a Grasstope arising from a totally positive linear map. While amplituhedra are relatively well-studied, much less is known about general Grasstopes. We study Grasstopes in the \\(m=1\\) case and show that they can be characterized as unions of cells of a hyperplane arrangement satisfying a certain sign variation condition, extending the work of Karp and Williams. Inspired by this characterization, we also suggest a notion of a Grasstope arising from an arbitrary oriented matroid.\n \nMathematics Subject Classifications: 05E14, 14N10, 14M15\n \nKeywords: Grasstope, Grassmannian, amplituhedron, hyperplane arrangements, sign vectors, oriented matroids",
    "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": "Grasstope"
        },
        {
            "word": "Grassmannian"
        },
        {
            "word": "amplituhedron"
        },
        {
            "word": "hyperplane arrangements"
        },
        {
            "word": "sign vectors"
        },
        {
            "word": "oriented matroids"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/71d8d238",
    "frozenauthors": [
        {
            "first_name": "Yelena",
            "middle_name": "",
            "last_name": "Mandelshtam",
            "name_suffix": "",
            "institution": "School of Mathematics, Institute for Advanced Study, Princeton, NJ, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Dmitrii",
            "middle_name": "",
            "last_name": "Pavlov",
            "name_suffix": "",
            "institution": "Faculty of Mathematics, TU Dresden, Dresden, Germany",
            "department": ""
        },
        {
            "first_name": "Elizabeth",
            "middle_name": "",
            "last_name": "Pratt",
            "name_suffix": "",
            "institution": "Department of Mathematics, UC Berkeley, Berkeley, CA, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2025-07-15T20:16:45+05:00",
    "date_accepted": "2025-07-15T20:16:45+05:00",
    "date_published": "2025-07-15T12:00:00+05:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64987/galley/49797/download/"
        }
    ]
}