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{
    "pk": 64989,
    "title": "A signed \\(e\\)-expansion of the chromatic quasisymmetric function",
    "subtitle": null,
    "abstract": "We prove a new signed elementary symmetric function expansion of the chromatic quasisymmetric function of any natural unit interval graph. We then use a sign-reversing involution to prove a new combinatorial formula for \\(K\\)-chains, which are graphs formed by joining cliques at single vertices. This formula immediately implies \\(e\\)-positivity and \\(e\\)-unimodality for \\(K\\)-chains. We also prove a version of our signed \\(e\\)-expansion for the chromatic symmetric function for arbitrary graphs.\n \nMathematics Subject Classifications: 05E05, 05E10, 05C15\n \nKeywords: Chromatic quasisymmetric function, elementary symmetric function, natural unit interval graph, proper colouring, Shareshian-Wachs conjecture, Stanley-Stembridge conjecture",
    "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": "Chromatic quasisymmetric function"
        },
        {
            "word": "elementary symmetric function"
        },
        {
            "word": "natural unit interval graph"
        },
        {
            "word": "proper colouring"
        },
        {
            "word": "Shareshian-Wachs conjecture"
        },
        {
            "word": "Stanley-Stembridge conjecture"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/9dc0v7wb",
    "frozenauthors": [
        {
            "first_name": "Foster",
            "middle_name": "",
            "last_name": "Tom",
            "name_suffix": "",
            "institution": "Department of Mathematics, Massachusetts Institute of Technology, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2025-07-16T00:21:12+09:00",
    "date_accepted": "2025-07-16T00:21:12+09:00",
    "date_published": "2025-07-15T16:00:00+09:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64989/galley/49799/download/"
        }
    ]
}