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{
    "pk": 64873,
    "title": "A combinatorial basis for the fermionic diagonal coinvariant ring",
    "subtitle": null,
    "abstract": "Let \\(\\Theta_n = (\\theta_1, \\dots, \\theta_n)\\) and \\(\\Xi_n = (\\xi_1, \\dots, \\xi_n)\\) be two lists of \\(n\\) variables and consider the diagonal action of \\(\\mathfrak{S}_n\\) on the exterior algebra \\(\\wedge \\{ \\Theta_n, \\Xi_n \\}\\) generated by these variables. Jongwon Kim and Rhoades defined and studied the fermionic diagonal coinvariant ring \\(FDR_n\\) obtained from \\(\\wedge \\{ \\Theta_n, \\Xi_n \\}\\) by modding out by the \\(\\mathfrak{S}_n\\)-invariants with vanishing constant term. The author and Rhoades gave a basis for the maximal degree components of this ring where the action of \\(\\mathfrak{S}_n\\) could be interpreted combinatorially via noncrossing set partitions. This paper will do similarly for the entire ring, although the combinatorial interpretation will be limited to the action of \\(\\mathfrak{S}_{n-1} \\subset \\mathfrak{S}_n\\). The basis will be indexed by a certain class of noncrossing partitions.\n \nMathematics Subject Classifications: 05E10, 05E18, 20C30\n \nKeywords: Skein relation, coinvariant algebra, noncrossing set partition, cyclic sieving",
    "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": "Skein relation"
        },
        {
            "word": "coinvariant algebra"
        },
        {
            "word": "noncrossing set partition"
        },
        {
            "word": "cyclic sieving"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/7nv8g68m",
    "frozenauthors": [
        {
            "first_name": "Jesse",
            "middle_name": "",
            "last_name": "Kim",
            "name_suffix": "",
            "institution": "Department of Mathematics, University of California, San Diego, La Jolla, CA, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2023-03-14T14:26:03Z",
    "date_accepted": "2023-03-14T14:26:03Z",
    "date_published": "2023-03-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64873/galley/49683/download/"
        }
    ]
}