Author: Tamás Schwarcz

The multiple exchange property for matroid bases states that for any bases $A$ and $B$ of a matroid and any subset $X\subseteq A\setminus B$, there exists a subset $Y\subseteq B\setminus A$ such that both $A-X+Y$ and $B+X-Y$ are bases. This classical result has not only found applications in matroid theory, but also in the analysis…

Consider a matroid equipped with a labeling of its ground set to an abelian group, and define the label of a subset of the ground set as the sum of the labels of its elements. In our paper Problems on group-labeled matroid bases, we study a collection of problems on finding bases and common bases…