Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Andrew Baxter**, Rutgers University, baxter{at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Balanced and Bruhat graphs

Speaker: **Margaret Readdy**, University of Kentucky (Member of the Institute for Advanced Study, 2010-2011)

Date: Thursday, December 2, 2010 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

The cd-index is a noncommutative polynomial which compactly encodes the flag vector data of the face lattice of a polytope, and more generally, 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 proves non-trivial inequalities among the face incidence data.

We consider a general class of labeled graphs which satisfy a balanced condition and develop the cd-index. As a special case, this work applies to Bruhat graphs arising from the strong Bruhat order on a Coxeter group and gives straightforward proofs of recent results of Billera and Brenti. I will also indicate various ongoing projects with Billera, Ehrenborg and Hetyei.