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{
    "pk": 64830,
    "title": "Odd diagrams, Bruhat order, and pattern avoidance",
    "subtitle": null,
    "abstract": "The odd diagram of a permutation is a subset of the classical diagram with additional parity conditions. In this paper, we study classes of permutations with the same odd diagram, which we call odd diagram classes. First, we prove a conjecture relating odd diagram classes and 213- and 312-avoiding permutations. Secondly, we show that each odd diagram class is a Bruhat interval. Instrumental to our proofs is an explicit description of the Bruhat edges that link permutations in a class.\n \nMathematics Subject Classifications: 05A05, 05A15",
    "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": "Odd diagram"
        },
        {
            "word": "Bruhat order"
        },
        {
            "word": "pattern avoidance"
        },
        {
            "word": "odd length"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/5pj7s2gq",
    "frozenauthors": [
        {
            "first_name": "Francesco",
            "middle_name": "",
            "last_name": "Brenti",
            "name_suffix": "",
            "institution": "Dipartimento di Matematica, Università di Roma \"Tor Vergata\", Via della Ricerca Scientifica 1, 00133 Roma, Italy",
            "department": ""
        },
        {
            "first_name": "Angela",
            "middle_name": "",
            "last_name": "Carnevale",
            "name_suffix": "",
            "institution": "School of Mathematical and Statistical Sciences, National University of Ireland, Galway, Ireland",
            "department": ""
        },
        {
            "first_name": "Bridget",
            "middle_name": "Eileen",
            "last_name": "Tenner",
            "name_suffix": "",
            "institution": "Department of Mathematical Sciences, DePaul University, Chicago, IL, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2022-03-23T20:38:49Z",
    "date_accepted": "2022-03-23T20:38:49Z",
    "date_published": "2022-03-31T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64830/galley/49640/download/"
        }
    ]
}