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{
    "pk": 64835,
    "title": "Stack-sorting for Coxeter groups",
    "subtitle": null,
    "abstract": "Given an essential semilattice congruence $\\equiv$ on the left weak order of a \\linebreak Coxeter group $W$, we define the Coxeter stack-sorting operator ${\\bf S}_\\equiv:W\\to W$ by ${{\\bf S}_\\equiv(w)=w\\big(\\pi_\\downarrow^\\equiv(w)\\big)^{-1}}$, where $\\pi_\\downarrow^\\equiv(w)$ is the unique minimal element of the congruence class of $\\equiv$ containing $w$. When $\\equiv$ is the sylvester congruence on the symmetric group $S_n$, the operator ${\\bf S}_\\equiv$ is West's stack-sorting map. When $\\equiv$ is the descent congruence on $S_n$, the operator ${\\bf S}_\\equiv$ is the pop-stack-sorting map. We establish several general results about Coxeter stack-sorting operators, especially those acting on symmetric groups. For example, we prove that if $\\equiv$ is an essential lattice congruence on $S_n$, then every permutation in the image of ${\\bf S}_\\equiv$ has at most $\\left\\lfloor\\frac{2(n-1)}{3}\\right\\rfloor$ right descents; we also show that this bound is tight.  We then introduce analogues of permutree congruences in types $B$ and $\\widetilde A$ and use them to isolate Coxeter stack-sorting operators $\\mathtt{s}_B$ and $\\widetilde{\\mathtt{s}}$ that serve as canonical type-$B$ and type-$\\widetilde A$ counterparts of West's stack-sorting map. We prove analogues of many known results about West's stack-sorting map for the new operators $\\mathtt{s}_B$ and $\\widetilde{\\mathtt{s}}$. For example, in type $\\widetilde A$, we obtain an analogue of Zeilberger's classical formula for the number of $2$-stack-sortable permutations in $S_n$.\n \nMathematics Subject Classifications: 06A12, 06B10, 37E15, 05A05, 05E16",
    "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": "Stack-sorting"
        },
        {
            "word": "Coxeter group"
        },
        {
            "word": "weak order"
        },
        {
            "word": "semilattice congruence"
        },
        {
            "word": "descent"
        },
        {
            "word": "valid hook configuration"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/34q9t2nn",
    "frozenauthors": [
        {
            "first_name": "Colin",
            "middle_name": "",
            "last_name": "Defant",
            "name_suffix": "",
            "institution": "Department of Mathematics, Princeton University, Princeton, New Jersey, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2022-03-23T21:15:24Z",
    "date_accepted": "2022-03-23T21:15:24Z",
    "date_published": "2022-03-31T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64835/galley/49645/download/"
        }
    ]
}