BIROn - Birkbeck Institutional Research Online

    Halfway to Rota's basis conjecture

    Bucić, M. and Kwan, M. and Pokrovskiy, Alexey and Sudakov, B. (2020) Halfway to Rota's basis conjecture. International Mathematics Research Notices 2020 (21), pp. 8007-8026. ISSN 1073-7928.

    [img]
    Preview
    Text
    1810.07462.pdf - Author's Accepted Manuscript

    Download (241kB) | Preview

    Abstract

    In 1989, Rota made the following conjecture. Given n bases B1,…,Bn in an n-dimensional vector space V, one can always find n disjoint bases of V, each containing exactly one element from each Bi (we call such bases transversal bases). Rota's basis conjecture remains wide open despite its apparent simplicity and the efforts of many researchers (for example, the conjecture was recently the subject of the collaborative "Polymath" project). In this paper we prove that one can always find (1/2−o(1))n disjoint transversal bases, improving on the previous best bound of Ω(n/logn). Our results also apply to the more general setting of matroids

    Metadata

    Item Type: Article
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Alexey Pokrovskiy
    Date Deposited: 20 Jan 2020 13:18
    Last Modified: 16 Jun 2021 10:19
    URI: https://eprints.bbk.ac.uk/id/eprint/30607

    Statistics

    Downloads
    Activity Overview
    5Downloads
    50Hits

    Additional statistics are available via IRStats2.

    Archive Staff Only (login required)

    Edit/View Item Edit/View Item