Article Instance

HTTP 200 OK
Allow: GET
Content-Type: application/json
Vary: Accept

{
    "pk": 64884,
    "title": "Set-valued tableaux rule for Lascoux polynomials",
    "subtitle": null,
    "abstract": "Lascoux polynomials generalize Grassmannian stable Grothendieck polynomials and may be viewed as K-theoretic analogs of key polynomials. The latter two polynomials have combinatorial formulas involving tableaux: Lascoux and Schützenberger gave a combinatorial formula for key polynomials using right keys; Buch gave a set-valued tableau formula for Grassmannian stable Grothendieck polynomials. We establish a novel combinatorial description for Lascoux polynomials involving right keys and set-valued tableaux. Our description generalizes the tableaux formulas of key polynomials and Grassmannian stable Grothendieck polynomials. To prove our description, we construct a new abstract Kashiwara crystal structure on set-valued tableaux. This construction answers an open problem of Monical, Pechenik and Scrimshaw.\n \nMathematics Subject Classifications: 05E05\n \nKeywords: Lascoux polynomials, set-valued tableaux, crystal operators",
    "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": "Lascoux polynomials"
        },
        {
            "word": "set-valued tableaux"
        },
        {
            "word": "crystal operators"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/2qp6q4w9",
    "frozenauthors": [
        {
            "first_name": "Tianyi",
            "middle_name": "",
            "last_name": "Yu",
            "name_suffix": "",
            "institution": "Department of Mathematics, UC San Diego, California, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2023-03-14T16:14:17Z",
    "date_accepted": "2023-03-14T16:14:17Z",
    "date_published": "2023-03-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64884/galley/49694/download/"
        }
    ]
}