Speaker:  Galen Dorpalen-Barry, Ruhr-Universität Bochum

Title:   The Poincaré-extended ab-index

Abstract:

Motivated by a conjecture of Maglione-Voll from group theory, we introduce and study the Poincaré-extended ab-index. This polynomial generalizes both the ab-index and the Poincaré polynomial.  For posets admitting R-labelings, we prove that the coefficients are nonnegative and give a combinatorial description of the coefficients. This proves Maglione-Voll's conjecture as well as a conjecture of the Kühne-Maglione. We also recover, generalize, and unify results from Billera-Ehrenborg-Readdy, Ehrenborg, and Saliola-Thomas.

This is joint work with Joshua Maglione and Christian Stump.

We will be meeting in 745 POT and the speaker will be live from Germany via Zoom.

Our website:  https://www.ms.uky.edu/~readdy/Seminar