Matroids from hypersimplex splits

摘要

A class of matroids is introduced which is very large as it strictly containsall paving matroids as special cases. As their key feature these split matroidscan be studied via techniques from polyhedral geometry. It turns out that thestructural properties of the split matroids can be exploited to obtain newresults in tropical geometry, especially on the rays of the tropicalGrassmannians.