The University of Michigan Combinatorics Seminar
Winter 2002
February 8, 4:10-5:00, 3866 East Hall

Inequalities satisfied by minors of totally nonnegative matrices

Mark Skandera

University of Michigan


A matrix is called totally nonnegative if each minor DI,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

DW,W' D X,X' < DY,Y' DZ,Z'

which hold for all totally nonnegative matrices. This generalizes recent work of Fallat, Gekhtman and Johnson.