University of Delaware
Discrete Mathematics Seminar

Weighted Planar Networks and Total Positivity
Shaun Fallat
University of Regina, Canada
Thursday, April 26, 2012
Ewing Hall 336 5.00 - 6.00 pm

Abstract: A matrix is called totally positive (nonnegative) if all of its minors are positive (nonnegative). This class of matrices has been studied for around a 100 years and has gone through a bit of a renaissance since the early 90's. This renewed interest is mostly due to an important and very useful combinatorial interpretation of these matrices. This combinatorial viewpoint is derived from a connection with weighted planar networks, which do have some history with these matrices.

I intend to review this connection between weighted planar networks and totally nonnegative matrices and discuss a number of key implications as a consequence of this viewpoint. I will close by describing a characterization, via planar networks, of all possible Jordan Canonical forms over the class of irreducible totally nonnegative matrices.