We will define elements in the space of symmetric functions and discuss a number of their classical properties revealing the role of combinatorics in this field. A filtration for the space will then be introduced and current results regarding a refinement of classical properties will be shown. We will finish by showing how our work with the filtration plays an interesting role in a long-standing open problem regarding the Macdonald symmetric functions.
Probability and Combinatorics
Tuesday, April 17, 2001 - 4:30pm
Jennifer Morse
University of Pennsylvania