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{
    "pk": 65009,
    "title": "An upper bound on the per-tile entropy of ribbon tilings",
    "subtitle": null,
    "abstract": "This paper considers \\(n\\)-ribbon tilings of general regions and their per-tile entropy (the binary logarithm of the number of tilings divided by the number of tiles). We show that the per-tile entropy is bounded above by \\(\\log_2 n\\). This bound improves the best previously known bounds of \\(n-1\\) for general regions, and the asymptotic upper bound of \\(\\log_2 (en)\\) for growing rectangles, due to Chen and Kargin.\n \nMathematics Subject Classifications: 05B45, 52C20\n \nKeywords: Ribbon tilings, domino tilings, dimer tilings",
    "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": "Ribbon tilings"
        },
        {
            "word": "domino tilings"
        },
        {
            "word": "dimer tilings"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/71b088cf",
    "frozenauthors": [
        {
            "first_name": "Simon",
            "middle_name": "R.",
            "last_name": "Blackburn",
            "name_suffix": "",
            "institution": "Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX, U.K.",
            "department": ""
        },
        {
            "first_name": "Yinsong",
            "middle_name": "",
            "last_name": "Chen",
            "name_suffix": "",
            "institution": "Department of Mathematics and Statistics, Binghamton University, Binghamton, New York, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Vladislav",
            "middle_name": "",
            "last_name": "Kargin",
            "name_suffix": "",
            "institution": "Department of Mathematics and Statistics, Binghamton University, Binghamton, New York, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2025-09-12T12:59:08Z",
    "date_accepted": "2025-09-12T12:59:08Z",
    "date_published": "2025-09-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/65009/galley/49819/download/"
        }
    ]
}