Discrete CATS Seminar
####
**
**#####
U N I V E R S I T Y O F K E N T U C K Y

DISCRETE
CATS
SEMINAR

WHERE CATS =
COMBINATORICS,
ALGEBRA,
TOPOLOGY
&
STATISTICS!

845 PATTERSON OFFICE TOWER

2008 - 2009

##
"Simplicial, cubical and cellular spanning trees"

Jeremy Martin

University of Kansas

###
Monday, April 13, 2009

4:00 pm, 845 Patterson Office Tower

####
Abstract:

The classical Matrix-Tree Theorem enumerates the number of spanning trees
in a graph; that is, the number of connected, acyclic subgraphs with one
fewer edge than it has vertices. Both the definition of spanning tree,
and the Matrix-Tree Theorem, can be generalized by replacing the graph
with a simplicial complex or even a CW-complex. For many kinds of
complexes (for example, shifted simplicial complexes and skeletons of
cubes), there are explicit combinatorial formulas for the number of
spanning trees, as well as generating functions that enumerate spanning
trees by some statistic such as vertex degree sequences. This is joint
work with Art Duval and Carly Klivans.