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Halfway to Rota's basis conjecture

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  • UserAlexey Pokrovskiy (Birkbeck, University of London)
  • ClockThursday 05 December 2019, 14:30-15:30
  • HouseMR12.

If you have a question about this talk, please contact Andrew Thomason.

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 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 talk, I will discuss how to find (0.5 – o(1))n disjoint transversal bases, improving the previously best known bound of n/log n. This is joint work with Bucic, Kwan, and Sudakov.

This talk is part of the Combinatorics Seminar series.

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