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{
    "pk": 65030,
    "title": "Poset polytopes and pipe dreams: types C and B",
    "subtitle": null,
    "abstract": "The first part of this paper concerns type C. We present new explicitly defined families of algebro-combinatorial structures of three kinds: combinatorial bases in representations, Newton-Okounkov bodies of flag varieties and toric degenerations of flag varieties. All three families are parametrized by the same family of polytopes: the marked chain-order polytopes of Fang and Fourier which interpolate between the type C Gelfand-Tsetlin and FFLV polytopes. Thus, in each case the obtained structures interpolate between the well-known bases, Newton-Okounkov bodies or degenerations associated with the latter two polytopes. We then obtain similar results for type B after introducing a new family of poset polytopes to be considered in place of marked chain-order polytopes. In both types our constructions and proofs rely crucially on a combinatorial connection between poset polytopes and pipe dreams.\n \nMathematics Subject Classifications: 14M15, 17B10, 05E14, 05E10, 52B20, 06A11\n \nKeywords: Flag varieties, poset polytopes, pipe dreams, toric degenerations, Newton– Okounkov bodies",
    "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": "Flag varieties"
        },
        {
            "word": "poset polytopes"
        },
        {
            "word": "pipe dreams"
        },
        {
            "word": "toric degenerations"
        },
        {
            "word": "Newton– Okounkov bodies"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/17d0m5pk",
    "frozenauthors": [
        {
            "first_name": "Ievgen",
            "middle_name": "",
            "last_name": "Makedonskyi",
            "name_suffix": "",
            "institution": "Beijing Institute of Mathematical Sciences and Applications (BIMSA), China",
            "department": ""
        },
        {
            "first_name": "Igor",
            "middle_name": "",
            "last_name": "Makhlin",
            "name_suffix": "",
            "institution": "Technische Universität Berlin, Institute of Mathematics, Chair of Discrete Mathematics/Geometry, Germany",
            "department": ""
        }
    ],
    "date_submitted": "2026-02-02T10:20:32Z",
    "date_accepted": "2026-02-02T10:20:32Z",
    "date_published": "2025-12-20T08:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/65030/galley/49840/download/"
        }
    ]
}