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{
    "pk": 64942,
    "title": "Generalized recursive atom ordering and equivalence to CL-shellability",
    "subtitle": null,
    "abstract": "Björner and Wachs introduced CL-shellability as a technique for studying the topological structure of order complexes of partially ordered sets. They also introduced the notion of recursive atom ordering, and they proved that a finite bounded poset is CL-shellable if and only if it admits a recursive atom ordering.\nIn this paper, a generalization of the notion of recursive atom ordering is introduced. A finite bounded poset is proven to admit such a generalized recursive atom ordering if and only if it admits a traditional recursive atom ordering. This is also proven equivalent to admitting a CC-shelling (a type of shelling introduced by Kozlov) with a further property called self-consistency. Thus, CL-shellability is proven equivalent to self-consistent CC-shellability. As an application, the uncrossing posets, namely the face posets for stratified spaces of planar electrical networks, are proven to be dual CL-shellable.\n \nMathematics Subject Classifications: 05E45, 06A07\n \nKeywords: Poset topology, lexicographic shellability, EC-shellability, recursive atom ordering,  uncrossing order",
    "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": "Poset topology"
        },
        {
            "word": "lexicographic shellability"
        },
        {
            "word": "EC-shellability"
        },
        {
            "word": "recursive atom ordering"
        },
        {
            "word": "uncrossing order"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/5242n3vj",
    "frozenauthors": [
        {
            "first_name": "Patricia",
            "middle_name": "",
            "last_name": "Hersh",
            "name_suffix": "",
            "institution": "Department of Mathematics, University of Oregon, Eugene, OR, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Grace",
            "middle_name": "",
            "last_name": "Stadnyk",
            "name_suffix": "",
            "institution": "Department of Mathematics, Furman University, Greenville SC, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2024-07-01T16:47:29+02:00",
    "date_accepted": "2024-07-01T16:47:29+02:00",
    "date_published": "2024-06-30T09:00:00+02:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64942/galley/49752/download/"
        }
    ]
}