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{
    "pk": 65015,
    "title": "Subsets of free groups with distinct differences",
    "subtitle": null,
    "abstract": "Let \\(F_n\\) be a free group of rank \\(n\\), with free generating set \\(X\\). A subset \\(D\\) of \\(F_n\\) is a Distinct Difference Configuration if the differences \\(g^{-1}h\\) are distinct, where \\(g\\) and \\(h\\) range over all (ordered) pairs of distinct elements of \\(D\\). The subset \\(D\\) has diameter at most \\(d\\) if these differences all have word length at most \\(d\\). When \\(n\\) is fixed and \\(d\\) is large, the paper shows that the largest distinct difference configuration in \\(F_n\\) of diameter at most \\(d\\) has size approximately \\((2n-1)^{d/3}\\).\n \nMathematics Subject Classifications: 05B10, 20E05\n \nKeywords: Difference sets, distinct difference configurations, free groups, combinatorial designs",
    "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": "Difference sets"
        },
        {
            "word": "distinct difference configurations"
        },
        {
            "word": "free groups"
        },
        {
            "word": "combinatorial designs"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/09j8n324",
    "frozenauthors": [
        {
            "first_name": "Simon",
            "middle_name": "R.",
            "last_name": "Blackburn",
            "name_suffix": "",
            "institution": "Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EZ, U.K.",
            "department": ""
        },
        {
            "first_name": "Emma",
            "middle_name": "K. A.",
            "last_name": "Smith",
            "name_suffix": "",
            "institution": "Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EZ, U.K.",
            "department": ""
        },
        {
            "first_name": "Luke",
            "middle_name": "D.J.",
            "last_name": "Stewart",
            "name_suffix": "",
            "institution": "Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EZ, U.K.",
            "department": ""
        }
    ],
    "date_submitted": "2026-02-02T08:46:22Z",
    "date_accepted": "2026-02-02T08:46:22Z",
    "date_published": "2025-12-20T08:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/65015/galley/49825/download/"
        }
    ]
}