Basis exchanges in split matroids

The basis exchange axiom has been a driving force in the development of matroid theory. In our recent paper titled Exchange distance of basis pairs in split matroids, we study the distance of basis pairs of a matroid in terms of symmetric exchanges. In particular, we give an upper bound on the minimum number of exchanges needed to transform a basis pair into another for split matroids. As a corollary, we verify long-standing conjectures of Gabow, White, and Farber for this large class. Being a subclass of split matroids, our result settles the conjectures for paving matroids as well.