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Rota's Basis Conjecture holds asymptotically

Pokrovskiy, Alexey; (2020) Rota's Basis Conjecture holds asymptotically. ArXiv Green open access

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Abstract

Rota's Basis Conjecture is a well known problem from matroid theory, that states that for any collection of n bases in a rank n matroid, it is possible to decompose all the elements into n disjoint rainbow bases. Here an asymptotic version of this is proved. We show that it is possible to find n−o(n) disjoint rainbow independent sets of size n−o(n).

Type: Working / discussion paper
Title: Rota's Basis Conjecture holds asymptotically
Open access status: An open access version is available from UCL Discovery
Publisher version: https://doi.org/10.48550/arXiv.2008.06045
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: math.CO, math.CO, 05B35, 05D15, G.2.1
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery-pp.ucl.ac.uk/id/eprint/10160843
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