Article Instance

HTTP 200 OK
Allow: GET
Content-Type: application/json
Vary: Accept

{
    "pk": 64801,
    "title": "Proof of the Kakeya set conjecture over rings of integers modulo square-free N",
    "subtitle": null,
    "abstract": "A Kakeya set $S \\subset (\\mathbb{Z}/N\\mathbb{Z})^n$ is a set containing a line in each direction. We show that, when $N$ is any square-free integer, the size of the smallest Kakeya set in $(\\mathbb{Z}/N\\mathbb{Z})^n$ is at least $C_{n,\\epsilon} N^{n - \\epsilon}$ for any $\\epsilon$ -- resolving a special case of a conjecture of Hickman and Wright. Previously, such bounds were only known for the case of prime $N$. We also show that the case of general $N$ can be reduced to lower bounding the $\\mathbb{F}_p$ rank of the incidence matrix of points and hyperplanes over $(\\mathbb{Z}/p^k\\mathbb{Z})^n$.\nMathematics Subject Classifications: 05B20, 05B25",
    "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": [],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/4324c8n4",
    "frozenauthors": [
        {
            "first_name": "Manik",
            "middle_name": "",
            "last_name": "Dhar",
            "name_suffix": "",
            "institution": "Department of Computer Science, Princeton University, Princeton, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Zeev",
            "middle_name": "",
            "last_name": "Dvir",
            "name_suffix": "",
            "institution": "Department of Computer Science and Department of Mathematics, Princeton University, Princeton, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2021-11-11T16:49:00Z",
    "date_accepted": "2021-11-11T16:49:00Z",
    "date_published": "2021-12-15T08:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64801/galley/49611/download/"
        }
    ]
}