Robin Sulzgruber: Cayley-Catalan combinatorics

Abstract

I will present several combinatorial objects counted by Catalan numbers (i.e., Dyck paths) or Cayley numbers (i.e., parking functions), and combinatorial maps between these objects. There exist many different ways to generalise such objects. For example, Dyck paths and parking functions both turn out to be special cases of more geometric objects attached to a root system. Our general goal is to unify as many different generalisations as possible. I will discuss some open problems in this field.