Samu Potka:The Cyclic Sieving Phenomenon on Circular Dyck Paths

Abstract:

Circular Dyck paths were recently studied by Alexandersson and Panova. We q-enumerated them and proved that they exhibit the cyclic sieving phenomenon (CSP) under shifting their area sequences. This is an example of special families of CSP instances which we call "Lyndon-like". I will discuss these results, and, if time permits, a similar CSP result on paths embedded on a Möbius strip as well as a generalization of the CSP called the subset cyclic sieving phenomenon. This is joint work with Per Alexandersson and Svante Linusson.