Enumerative combinatorics
Dual equivalence with applications, including a conjecture of Proctor
Discrete Mathematics - Special volume: algebraic combinatorics
On the Fully Commutative Elements of Coxeter Groups
Journal of Algebraic Combinatorics: An International Journal
Dynkin Diagram Classification of λ-Minuscule Bruhat Latticesand of d-Complete Posets
Journal of Algebraic Combinatorics: An International Journal
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We study the reduced expressions for reflections in Coxeter groups, with particular emphasis on finite Weyl groups. For example, the number of reduced expressions for any reflection can be expressed as the sum of the squares of the number of reduced expressions for certain elements naturally associated to the reflection. In the case of the longest reflection in a Weyl group, we use a theorem of Dale Peterson to provide an explicit formula for the number of reduced expressions. We also show that the reduced expressions for any Weyl group reflection are in bijection with the linear extensions of a natural partial ordering of a subset of the positive roots or co-roots.