The University of Michigan Combinatorics Seminar


Abstract 

A matrix is called totally nonnegative if each minor
D_{I,I'} (the determinant of the submatrix corresponding
to row set I and column set I') is nonnegative.
A well known combinatorial interpretation of the minors of totally
nonnegative matrices
involves families of paths in planar networks.
Using planar networks, we will
characterize all inequalities of the form
which hold for all totally nonnegative matrices. This generalizes recent work of Fallat, Gekhtman and Johnson. 