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{
    "pk": 64883,
    "title": "Chain enumeration, partition lattices and polynomials with only real roots",
    "subtitle": null,
    "abstract": "The coefficients of the chain polynomial of a finite poset enumerate chains in the poset by their number of elements. The chain polynomials of the partition lattices and their standard type \\(B\\) analogues are shown to have only real roots. The real-rootedness of the chain polynomial is conjectured for all geometric lattices and is shown to be preserved by the pyramid and the prism operations on Cohen-Macaulay posets. As a result, new families of convex polytopes whose barycentric subdivisions have real-rooted \\(f\\)-polynomials are presented. An application to the face enumeration of the second barycentric subdivision of the boundary complex of the simplex is also included.\n \nMathematics Subject Classifications: 05A05, 05A18, 05E45, 06A07, 26C10\n \nKeywords: Chain polynomial, geometric lattice, partition lattice,  real-rooted polynomial, flag \\(h\\)-vector, convex polytope, barycentric  subdivision",
    "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": "Chain polynomial"
        },
        {
            "word": "geometric lattice"
        },
        {
            "word": "partition lattice"
        },
        {
            "word": "real-rooted polynomial"
        },
        {
            "word": "flag \\(h\\)-vector"
        },
        {
            "word": "convex polytope"
        },
        {
            "word": "barycentric  subdivision"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/5nh7x8kr",
    "frozenauthors": [
        {
            "first_name": "Christos",
            "middle_name": "A.",
            "last_name": "Athanasiadis",
            "name_suffix": "",
            "institution": "Department of Mathematics, National and Kapodistrian University of Athens, 15784 Athens, Greece",
            "department": ""
        },
        {
            "first_name": "Katerina",
            "middle_name": "",
            "last_name": "Kalampogia-Evangelinou",
            "name_suffix": "",
            "institution": "Department of Mathematics, National and Kapodistrian University of Athens, 15784 Athens, Greece",
            "department": ""
        }
    ],
    "date_submitted": "2023-03-14T16:11:38Z",
    "date_accepted": "2023-03-14T16:11:38Z",
    "date_published": "2023-03-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64883/galley/49693/download/"
        }
    ]
}