Some combinatorial models for reduced expressionsHugh Denoncourt, CU |
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October 28 AbstractStanley'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. It will be shown that this construction generalizes the balanced labellings of Fomin et al. The framework also provides a formula for the length of an element formed by deleting a generator from a Coxeter group element. |