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{
    "pk": 64893,
    "title": "Rectangular analogues of the square paths conjecture and the univariate Delta conjecture",
    "subtitle": null,
    "abstract": "In this paper, we extend the rectangular side of the shuffle conjecture by stating a rectangular analogue of the square paths conjecture. In addition, we describe a set of combinatorial objects and one statistic that are a first step towards a rectangular extension of (the rise version of) the Delta conjecture, and of (the rise version of) the Delta square conjecture, corresponding to the case \\(q=1\\) of an expected general statement. We also prove our new rectangular paths conjecture in the special case when the sides of the rectangle are coprime.\n \nMathematics Subject Classifications: 05E05\n \nKeywords: Macdonald polynomials, symmetric functions",
    "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": "Macdonald polynomials"
        },
        {
            "word": "symmetric functions"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/53s7m4h3",
    "frozenauthors": [
        {
            "first_name": "Alessandro",
            "middle_name": "",
            "last_name": "Iraci",
            "name_suffix": "",
            "institution": "Dipartimento di Matematica, Università di Pisa, Pisa, Italy",
            "department": ""
        },
        {
            "first_name": "Roberto",
            "middle_name": "",
            "last_name": "Pagaria",
            "name_suffix": "",
            "institution": "Dipartimento di Matematica, Università di Bologna, Bologna, Italy",
            "department": ""
        },
        {
            "first_name": "Giovanni",
            "middle_name": "",
            "last_name": "Paolini",
            "name_suffix": "",
            "institution": "California Institute of Technology, Pasadena CA, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Anna",
            "middle_name": "",
            "last_name": "Vanden Wyngaerd",
            "name_suffix": "",
            "institution": "Département de Mathématique, Université Libre de Bruxelles, Bruxelles, Belgium",
            "department": ""
        }
    ],
    "date_submitted": "2023-09-13T16:06:45Z",
    "date_accepted": "2023-09-13T16:06:45Z",
    "date_published": "2023-09-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64893/galley/49703/download/"
        }
    ]
}