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Character Polynomials and Lagrange Inversion

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arattan2005.pdf (781.74 KB)

Date

2005

Authors

Rattan, Amarpreet

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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.

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Keywords

Mathematics, representation theory, algebra, lagrange inversion, polynomials, generating series

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URI

http://hdl.handle.net/10012/1029

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Combinatorics and Optimization