Finite matchability under the matroidal Hall's condition

Abstract

Aharoni and Ziv conjectured that if $M$ and $N$ are finitary matroids on $E$, then a certain ``Hall-like'' condition is sufficient to guarantee the existence of an $M$-independent spanning set of $N$. We show that their condition ensures that every finite subset of $E$ is $N$-spanned by an $M$-independent set.