Nonnegative minors of minor matrices

Abstract

Using the relationship between totally nonnegative matrices and directed acyclic weighted planar networks, we show that $2\times 2$ minors of minor matrices of totally nonnegative matrices are also nonnegative. We give a combinatorial interpretation for the minors of minor matrices in terms of the weights of families of paths in a network.

References in corpus (2)

• Total positivity, Grassmannians, and networks
• Iterated sequences and the geometry of zeros