"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.