Some Automatic Combinatorics using Symmetric Functions and Maple
Marni Mishna, Mathematics, SFU
Abstract: One can calculate enumerative formulas for some graph-like families of combinatorial objects using symmetric functions and symmetric series. The widely used SF package for Maple, developed by John Stembridge, is extremely useful for basic manipulation of symmetric functions, and can give some small enumerative results in this context. This talk will describe a new Maple package, which is designed to calculate symmetric function operations on a symmetric series scale, which will allow us to compute generating function information. We shall further illustrate how the routines in the package can be incorporated into a semi-automated scheme for the asymptotic enumeration of regular graphs and hypergraphs, amongst other related objects. If time permits, we will also show a method for symbolically proving some new symmetric function identities using the same package.