University
of Northern Iowa Department of Mathematics
Title: The Pfaffian Matrix-tree Theorem
Speaker: Scott Hirschman
ABSTRACT
Kirchoff's
celebrated Matrix-Tree Theorem gives a determinant counting spanning
trees in a graph. Recently Masbaum and Vaintrob proved an
analogue of the Matrix-Tree Theorem giving a Pfaffian that enumerates
spanning trees in a 3-uniform hypergraph. At the University of
Minnesota Research Experience for Undergraduates, Vic Reiner and
myself created another proof of this pfaffian version of the
matrix-tree theorem by way of sign-reversing involution.