Article Instance

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

{
    "pk": 64866,
    "title": "Pop-stack-sorting for Coxeter groups",
    "subtitle": null,
    "abstract": "Let \\(W\\) be an irreducible Coxeter group. We define the Coxeter pop-stack-sorting operator \\(\\mathsf{Pop}:W\\to W\\) to be the map that fixes the identity element and sends each nonidentity element \\(w\\) to the meet of the elements covered by \\(w\\) in the right weak order. When \\(W\\) is the symmetric group \\(S_n\\), \\(\\mathsf{Pop}\\) coincides with the pop-stack-sorting map. Generalizing a theorem about the pop-stack-sorting map due to Ungar, we prove that \\[\\sup\\limits_{w\\in W}\\left|O_{\\mathsf{Pop}}(w)\\right|=h,\\] where \\(h\\) is the Coxeter number of \\(W\\) (with \\(h=\\infty\\) if \\(W\\) is infinite) and \\(O_f(w)\\) denotes the forward orbit of \\(w\\) under a map \\(f\\). When \\(W\\) is finite, this result is equivalent to the statement that the maximum number of terms appearing in the Brieskorn normal form of an element of \\(W\\) is \\(h-1\\). More generally, we define a map \\(f:W\\to W\\) to be compulsive if for every \\(w\\in W\\), \\(f(w)\\) is less than or equal to \\(\\mathsf{Pop}(w)\\) in the right weak order. We prove that if \\(f\\) is compulsive, then \\(\\sup\\limits_{w\\in W}|O_f(w)|\\leq h\\). This result is new even for symmetric groups.  We prove that \\(2\\)-pop-stack-sortable elements in type \\(B\\) are in bijection with \\(2\\)-pop-stack-sortable permutations in type \\(A\\), which were enumerated by Pudwell and Smith. Claesson and Gu{\\dh}mundsson proved that for each fixed nonnegative integer \\(t\\), the generating function that counts \\(t\\)-pop-stack-sortable permutations in type \\(A\\) is rational; we establish analogous results in types \\(B\\) and \\(\\widetilde A\\).\n \nMathematics Subject Classifications: 05E16, 37E15, 05A05\n \nKeywords: Pop-stack-sorting, Coxeter group, weak order, Coxeter number, compulsive map, regular language",
    "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": "Pop-stack-sorting"
        },
        {
            "word": "Coxeter group"
        },
        {
            "word": "weak order"
        },
        {
            "word": "Coxeter number"
        },
        {
            "word": "compulsive map"
        },
        {
            "word": "regular language"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/0n9037xd",
    "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": "2022-10-12T14:21:57Z",
    "date_accepted": "2022-10-12T14:21:57Z",
    "date_published": "2022-10-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64866/galley/49676/download/"
        }
    ]
}