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.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OWTU.10012/1029 |
| Date | January 2005 |
| Creators | Rattan, Amarpreet |
| Publisher | University of Waterloo |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Rights | Copyright: 2005, Rattan, Amarpreet. All rights reserved. |
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