Kelli Talaska

A generalization of Lindstrom's Lemma, via planar networks and the real Grassmannian

Lindstrom's Lemma, popularized by Gessel and Viennot, is a classical result which relates certain determinants to enumerations of non-crossing path families in acyclic directed graphs. In this talk, we will give a natural generalization to directed graphs which are not necessarily acyclic, based on Postnikov's work establishing a relationship between certain planar networks and points in the appropriate real Grassmannian. The talk will be elementary, with plenty of examples.