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arXiv · 2008.06045

Rota's Basis Conjecture holds asymptotically

Alexey Pokrovskiy
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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 $n-o(n)$.

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Alexey Pokrovskiy. 2020-08-13. Rota's Basis Conjecture holds asymptotically. https://arxiv.org/abs/2008.06045

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