Analysis of the Kerov–Olshanski Algebra
In this chapter, we investigate the algebra of polynomial functions in coordinates of Young diagrams as a nice framework in which various quantities on Young diagrams can be efficiently computed. This algebra was introduced by Kerov–Olshanski , analysis of which is substantially due to Ivanov–Olshanski . Several systems of generators and associated generating functions are considered. It is important to understand the concrete transition rules between these generating systems, one of which is the Kerov polynomial.