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- W2895963723 abstract "In 1989, Rota made the following conjecture. Given $n$ bases $B_{1},dots,B_{n}$ in an $n$-dimensional vector space $V$, one can always find $n$ disjoint bases of $V$, each containing exactly one element from each $B_{i}$ (we call such bases transversal bases). Rota's basis conjecture remains wide 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 paper we prove that one can always find $left(1/2-oleft(1right)right)n$ disjoint transversal bases, improving on the previous best bound of $Omegaleft(n/log nright)$. Our results also apply to the more general setting of matroids." @default.
- W2895963723 created "2018-10-26" @default.
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- W2895963723 date "2018-10-17" @default.
- W2895963723 modified "2023-09-27" @default.
- W2895963723 title "Halfway to Rota's basis conjecture." @default.
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