Rota's basis conjecture holds asymptotically

Rota's basis conjecture holds asymptotically

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Alexey Pokrovskiy, Birkbeck College

Rota's basis conjecture is a well-known problem, 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 will be discussed - that it is possible to find n − o(n) disjoint rainbow independent sets of size n − o(n).