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{
    "pk": 64876,
    "title": "Proof of a bi-symmetric septuple equidistribution on ascent sequences",
    "subtitle": null,
    "abstract": "It is well known since the seminal work by Bousquet-Mélou, Claesson, Dukes and Kitaev (2010) that certain refinements of the ascent sequences with respect to several natural statistics are in bijection with corresponding refinements of \\(({\\bf2+2})\\)-free posets and permutations that avoid a bi-vincular pattern. Different multiply-refined enumerations of ascent sequences and other bijectively equivalent structures have subsequently been extensively studied by various authors. In this paper, our main contributions are\na bijective proof of a bi-symmetric septuple equidistribution of Euler-Stirling statistics on ascent sequences, involving the number of ascents (\\(\\mathsf{asc}\\)), the number of repeated entries (\\(\\mathsf{rep}\\)), the number of zeros (\\(\\mathsf{zero}\\)), the number of maximal entries (\\(\\mathsf{max}\\)), the number of right-to-left minima (\\(\\mathsf{rmin}\\)) and two auxiliary statistics;\n \na new transformation formula for non-terminating basic hypergeometric \\(_4\\phi_3\\) series expanded as an analytic function in base \\(q\\) around \\(q=1\\), which is utilized to prove two (bi)-symmetric quadruple equidistributions on ascent sequences.\n \n A by-product of our findings includes the affirmation of a conjecture about the bi-symmetric equidistribution between the quadruples of Euler-Stirling statistics \\((\\mathsf{asc},\\mathsf{rep},\\mathsf{zero},\\mathsf{max})\\) and \\((\\mathsf{rep},\\mathsf{asc},\\mathsf{max},\\mathsf{zero})\\) on ascent sequences, that was motivated by a double Eulerian equidistribution due to Foata (1977) and recently proposed by Fu, Lin, Yan, Zhou and the first author (2018).\n \n \nMathematics Subject Classifications: 05A15, 05A19\n \nKeywords: Ascent sequences, equidistributions, Euler-Stirling statistics, Fishburn numbers, basic hypergeometric series",
    "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": "Ascent sequences"
        },
        {
            "word": "equidistributions"
        },
        {
            "word": "Euler-Stirling statistics"
        },
        {
            "word": "Fishburn numbers"
        },
        {
            "word": "basic hypergeometric series"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/3225t6v2",
    "frozenauthors": [
        {
            "first_name": "Emma",
            "middle_name": "Yu",
            "last_name": "Jin",
            "name_suffix": "",
            "institution": "School of Mathematical Sciences, Xiamen University, Xiamen, China",
            "department": ""
        },
        {
            "first_name": "Michael",
            "middle_name": "J.",
            "last_name": "Schlosser",
            "name_suffix": "",
            "institution": "Fakultät für Mathematik, Universität Wien, Vienna, Austria",
            "department": ""
        }
    ],
    "date_submitted": "2023-03-14T15:24:17Z",
    "date_accepted": "2023-03-14T15:24:17Z",
    "date_published": "2023-03-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64876/galley/49686/download/"
        }
    ]
}