Character Polynomials and Lagrange Inversion
Loading...
Date
2005
Authors
Rattan, Amarpreet
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
In this thesis, we investigate two expressions for symmetric group characters: Kerov?s universal character polynomials and Stanley?s character polynomials. We give a new explicit form for Kerov?s polynomials, which exactly evaluate the characters of the symmetric group scaled by degree and a constant. We use this explicit expression to obtain specific information about Kerov polynomials, including partial answers to positivity questions. We then use the expression obtained for Kerov?s polynomials to obtain results about Stanley?s character polynomials.
Description
Keywords
Mathematics, representation theory, algebra, lagrange inversion, polynomials, generating series