Word combinatorics for Coxeter groups IHugh Denoncourt, CU |
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April 21, 2009 AbstractMany combinatorial questions that arise in the context of Coxeter groups rely on properties of reduced expressions for a Coxeter group element. We present a discrete geometric model for arbitrary Coxeter group elements of arbitrary Coxeter groups and show that the model can be used to answer questions about reduced expressions. In particular, we can ascertain the effect of deleting a generator from a reduced expression upon the length of a Coxeter group element. Additionally, we construct correspondences between reduced expressions of an element and tournaments placed "on top" of the element's discrete geometric model. |