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{
    "pk": 64828,
    "title": "The non-existence of block-transitive subspace designs",
    "subtitle": null,
    "abstract": "Let $q$ be a prime power and $V\\cong\\mathbb{F}_q^d$. A $t$-$(d,k,\\lambda)_q$ design, or simply a subspace design, is a pair $\\mathcal{D}=(V,\\mathcal{B})$, where $\\mathcal{B}$ is a subset of the set of all $k$-dimensional subspaces of $V$, with the property that each $t$-dimensional subspace of $V$ is contained in precisely $\\lambda$ elements of $\\mathcal{B}$. Subspace designs are the $q$-analogues of balanced incomplete block designs. Such a design is called block-transitive if its automorphism group $\\mathrm{Aut}(\\mathcal{D})$ acts transitively on $\\mathcal{B}$. It is shown here that if $t\\geq 2$ and $\\mathcal{D}$ is a block-transitive $t$-$(d,k,\\lambda)_q$ design then $\\mathcal{D}$ is trivial, that is, $\\mathcal{B}$ is the set of all $k$-dimensional subspaces of $V$.\n \nMathematics Subject Classifications: 05E18, 05B99",
    "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": "Subspace designs"
        },
        {
            "word": "$q$-analogue"
        },
        {
            "word": "block-transitive"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/66t045d3",
    "frozenauthors": [
        {
            "first_name": "Daniel",
            "middle_name": "R.",
            "last_name": "Hawtin",
            "name_suffix": "",
            "institution": "Faculty of Mathematics, University of Rijeka, Rijeka, Croatia.",
            "department": ""
        },
        {
            "first_name": "Jesse",
            "middle_name": "",
            "last_name": "Lansdown",
            "name_suffix": "",
            "institution": "Centre for the Mathematics of Symmetry and Computation, The University of Western Australia, Perth, Australia.",
            "department": ""
        }
    ],
    "date_submitted": "2022-03-23T20:24:11Z",
    "date_accepted": "2022-03-23T20:24:11Z",
    "date_published": "2022-03-31T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64828/galley/49638/download/"
        }
    ]
}