Halfway to Rota’s basis conjecture

Bucić M, Kwan MA, Pokrovskiy A, Sudakov B. 2020. Halfway to Rota’s basis conjecture. International Mathematics Research Notices. 2020(21), 8007–8026.


Journal Article | Published | English

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Author
Bucić, Matija; Kwan, Matthew AlanIST Austria; Pokrovskiy, Alexey; Sudakov, Benny
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 (e.g., 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.
Publishing Year
Date Published
2020-11-01
Journal Title
International Mathematics Research Notices
Volume
2020
Issue
21
Page
8007-8026
ISSN
eISSN
IST-REx-ID

Cite this

Bucić M, Kwan MA, Pokrovskiy A, Sudakov B. Halfway to Rota’s basis conjecture. International Mathematics Research Notices. 2020;2020(21):8007-8026. doi:10.1093/imrn/rnaa004
Bucić, M., Kwan, M. A., Pokrovskiy, A., & Sudakov, B. (2020). Halfway to Rota’s basis conjecture. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnaa004
Bucić, Matija, Matthew Alan Kwan, Alexey Pokrovskiy, and Benny Sudakov. “Halfway to Rota’s Basis Conjecture.” International Mathematics Research Notices. Oxford University Press, 2020. https://doi.org/10.1093/imrn/rnaa004.
M. Bucić, M. A. Kwan, A. Pokrovskiy, and B. Sudakov, “Halfway to Rota’s basis conjecture,” International Mathematics Research Notices, vol. 2020, no. 21. Oxford University Press, pp. 8007–8026, 2020.
Bucić M, Kwan MA, Pokrovskiy A, Sudakov B. 2020. Halfway to Rota’s basis conjecture. International Mathematics Research Notices. 2020(21), 8007–8026.
Bucić, Matija, et al. “Halfway to Rota’s Basis Conjecture.” International Mathematics Research Notices, vol. 2020, no. 21, Oxford University Press, 2020, pp. 8007–26, doi:10.1093/imrn/rnaa004.
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