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{
    "pk": 65037,
    "title": "Structure of quasi-crystal graphs and applications to the combinatorics of quasi-symmetric functions",
    "subtitle": null,
    "abstract": "Crystal graphs are powerful combinatorial tools for working with the plactic monoid and symmetric functions. Quasi-crystal graphs are an analogous concept for the hypoplactic monoid and quasi-symmetric functions. This paper makes a combinatorial study of these objects. We explain a previously-observed isomorphism of components of the quasi-crystal graph, and provide an explicit description using a new combinatorial structure called a quasi-array. Then two conjectures of Maas-Gariépy on the interaction of fundamental quasi-symmetric functions and Schur functions and on the arrangement of quasi-crystal components within crystal components are answered, the former positively, the latter negatively.\n \nMathematics Subject Classifications: 05E05, 05E99\n \nKeywords: Crystal graphs, quasi-crystal graphs, quasi-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": "Crystal graphs"
        },
        {
            "word": "quasi-crystal graphs"
        },
        {
            "word": "quasi-symmetric functions"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/9mc8924r",
    "frozenauthors": [
        {
            "first_name": "Alan",
            "middle_name": "J.",
            "last_name": "Cain",
            "name_suffix": "",
            "institution": "Center for Mathematics and Applications (NOVA Math), NOVA School of Science and Technology, NOVA University of Lisbon, Portugal",
            "department": ""
        },
        {
            "first_name": "António",
            "middle_name": "",
            "last_name": "Malheiro",
            "name_suffix": "",
            "institution": "Center for Mathematics and Applications (NOVA Math) / Department of Mathematics, NOVA School of Science and Technology, NOVA University of Lisbon, Portugal",
            "department": ""
        },
        {
            "first_name": "Fátima",
            "middle_name": "",
            "last_name": "Rodrigues",
            "name_suffix": "",
            "institution": "Center for Mathematics and Applications (NOVA Math) / Department of Mathematics, NOVA School of Science and Technology, NOVA University of Lisbon, Portugal",
            "department": ""
        },
        {
            "first_name": "Inês",
            "middle_name": "",
            "last_name": "Rodrigues",
            "name_suffix": "",
            "institution": "Center for Mathematics and Applications (NOVA Math), NOVA School of Science and Technology, NOVA University of Lisbon, Portugal",
            "department": ""
        }
    ],
    "date_submitted": "2026-04-20T12:20:41-07:00",
    "date_accepted": "2026-04-20T12:20:41-07:00",
    "date_published": "2026-04-20T00:00:00-07:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/65037/galley/49847/download/"
        }
    ]
}