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

##
"The cd-index of Bruhat and balanced graphs"

Margaret A. Readdy

University of Kentucky

###
Monday, January 26, 2009

4:00 pm, 845 Patterson Office Tower

####
Abstract:

The cd-index is a noncommutative polynomial which compactly encodes
the flag vector data of an Eulerian poset. There is a simple yet
powerful coalgebraic structure on the cd-index which enables one to
understand how the cd-index of a polytope changes under geometric
operations and prove non-trivial inequalities among the face incidence
data.

Billera and Brenti have recently developed the notion of the
"complete" cd-index for Bruhat graphs. Although maximal chains in the
Bruhat graph are not all the same length, one can nevertheless define
an extended cd-index. Motivated by their work, we consider a more
general class of labeled graphs which satisfy a balanced condition and
develop the cd-index.

This is joint work-in-progress with Richard Ehrenborg.