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{
    "pk": 65003,
    "title": "Harmonious sequences in groups with a unique involution",
    "subtitle": null,
    "abstract": "We study several combinatorial properties of finite groups that are related to the notions of sequenceability, R-sequenceability, and harmonious sequences. In particular, we show that in every abelian group \\(G\\) with a unique involution \\(\\imath_G\\) there exists a permutation \\(g_0,\\ldots, g_{m}\\) of elements of \\(G \\backslash \\{\\imath_G\\}\\) such that the consecutive sums \\({g_0+g_1, g_1+g_2,\\ldots, g_{m}+g_0}\\) also form a permutation of elements of \\(G\\backslash \\{\\imath_G\\}\\). We also show that in every abelian group of order at least 4 there exists a sequence containing each non-identity element of \\(G\\) exactly twice such that the consecutive sums also contain each non-identity element of \\(G\\) twice. We apply several results to the existence of transversals in Latin squares.\n \nMathematics Subject Classifications: 05E16, 20D60, 05B15\n \nKeywords: Sequenceable groups, Latin squares, harmonious groups, complete mappings",
    "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": "Sequenceable groups"
        },
        {
            "word": "Latin squares"
        },
        {
            "word": "harmonious groups"
        },
        {
            "word": "complete mappings"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/5489614t",
    "frozenauthors": [
        {
            "first_name": "Lydia",
            "middle_name": "",
            "last_name": "de Wolf",
            "name_suffix": "",
            "institution": "Department of Mathematics, Siena University, NY, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Mohammad",
            "middle_name": "",
            "last_name": "Javaheri",
            "name_suffix": "",
            "institution": "Department of Mathematics, Siena University, NY, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2025-09-12T11:54:36Z",
    "date_accepted": "2025-09-12T11:54:36Z",
    "date_published": "2025-09-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/65003/galley/49813/download/"
        }
    ]
}