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Dissertation/Thesis Abstract

Some combinatorial models for reduced expressions in Coxeter groups
by Denoncourt, Hugh, Ph.D., University of Colorado at Boulder, 2009, 117; 3366660
Abstract (Summary)

Stanley's formula for the number of reduced expressions of a permutation regarded as a Coxeter group element raises the question of how to enumerate the reduced expressions of an arbitrary Coxeter group element. We provide a framework for answering this question by constructing combinatorial objects that represent the inversion set and the reduced expressions for an arbitrary Coxeter group element. The framework also provides a formula for the length of an element formed by deleting a generator from a Coxeter group element. Fan and Hagiwara, et al: showed that for certain Coxeter groups, the short-braid avoiding elements characterize those elements that give reduced expressions when any generator is deleted from a reduced expression. We provide a characterization that holds in all Coxeter groups. Lastly, we give applications to the freely braided elements introduced by Green and Losonczy, generalizing some of their results that hold in simply-laced Coxeter groups to the arbitrary Coxeter group setting.

Indexing (document details)
Advisor: Green, Richard M., Thiem, Nathaniel
Commitee: Finkelstein, Noah, Liebler, Robert, Vojtechovsky, Petr
School: University of Colorado at Boulder
Department: Mathematics
School Location: United States -- Colorado
Source: DAI-B 70/07, Dissertation Abstracts International
Subjects: Mathematics
Keywords: Coxeter groups, Enumeration, Freely braided, Fully covering, Reduced expressions, Reflection subgroups
Publication Number: 3366660
ISBN: 978-1-109-28232-0
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