# base

## Rota's basis conjecture ★★★

Author(s): Rota

\begin{conjecture} Let $V$ be a vector space of dimension $n$ and let $B_1,\ldots,B_n \subseteq V$ be bases. Then there exist $n$ disjoint transversals of $B_1,\ldots,B_n$ each of which is a base. \end{conjecture}

Keywords: base; latin square; linear algebra; matroid; transversal