Some Automatic Combinatorics using Symmetric Functions and Maple

Marni Mishna, Mathematics, SFU

Wednesday December 14th, 2005 at 3:30pm in K9509.

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.