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{
    "pk": 65039,
    "title": "Shuffle bases and quasisymmetric power sums",
    "subtitle": null,
    "abstract": "The algebra of quasisymmetric functions QSym and the shuffle algebra of compositions Sh are isomorphic as graded Hopf algebras (in characteristic zero), and isomorphisms between them can be specified via shuffle bases of QSym. We use the notion of infinitesimal characters to characterize shuffle bases, and we establish a universal property for Sh in the category of connected graded Hopf algebras equipped with an infinitesimal character, analogous to the universal property of QSym as a combinatorial Hopf algebra described by Aguiar, Bergeron, and Sottile. We then use these results to give general constructions for quasisymmetric power sums, recovering four previous constructions from the literature, and study their properties.\n \nMathematics Subject Classifications: 05E05, 16T30\n \nKeywords: Quasisymmetric functions, quasisymmetric power sums, shuffle algebra, compositions, infinitesimal characters",
    "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": "Quasisymmetric functions"
        },
        {
            "word": "quasisymmetric power sums"
        },
        {
            "word": "shuffle algebra"
        },
        {
            "word": "compositions"
        },
        {
            "word": "infinitesimal characters"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/6qn3s2sw",
    "frozenauthors": [
        {
            "first_name": "Ricky",
            "middle_name": "Ini",
            "last_name": "Liu",
            "name_suffix": "",
            "institution": "Department of Mathematics, University of Washington, Seattle, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Michael",
            "middle_name": "S.",
            "last_name": "Tang",
            "name_suffix": "",
            "institution": "Department of Mathematics, University of Washington, Seattle, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2026-04-20T12:25:58-07:00",
    "date_accepted": "2026-04-20T12:25:58-07:00",
    "date_published": "2026-04-20T00:00:00-07:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/65039/galley/49849/download/"
        }
    ]
}