Symmetric Functions and P-Recursiveness

Symmetric functions are a very powerful algebraic and combinatorial tool. Simple operations like specializing variables can yield interesting, complex formulas. Further, by expressing symmetric functions in terms of certain bases, followed by coefficient extraction we can obtain solutions to enumerative problems. The principal aim of this talk is to review the rich and important article "Symmetric Functions and P-Recursiveness" by I. Gessel. The concentration will be on the manipulation of symmetric functions to derive combinatorial formulas with an eye on how to generalise his techniques. We will define D-finite and P-recursive in this context and then examine the application to Young tableaux of bounded height.