Christian Stump (Ruhr Universität Bochum): Polynomials are great combinatorial invariants

Zoom-Link: https://uni-kassel.zoom-x.de/j/62202241000?pwd=JRmQYtmTfbXQat38ZKv7ycVbROMMuB.1

Meeting-ID: 622 0224 1000

Kenncode: 947084

4:45 PM – Cookies and Coffee (Room 1404)

Abstract:

In this talk, I present several invariants that one can associate to a finite graded bounded poset. These include the Möbius function, characteristic polynomial, incidence algebra, chain polynomial, ab-index, and (flag) f- and h-vectors. I also present recently defined families of polynomials associated to such a poset that gained a lot of attention in algebraic combinatorics: the Poincaré-extended ab-index, flag coarse Hilbert-Poincaré series, and Chow polynomial. I discuss their properties such as their unimodality, log-concavity, gamma-positivity, and real-rootedness.

We look forward to welcoming you!

Sincerely,

T. Mütze