Séminaire Lotharingien de Combinatoire, 80B.51 (2018), 12 pp.
Joel Brewster Lewis, Jon
McCammond, T. Kyle
Petersen and Petra
Schwer
Computing Reflection Length in an Affine Coxeter Group
Abstract.
In any Coxeter group, the conjugates of elements in its Coxeter
generating set are called reflections and the reflection length of
an element is its length with respect to this expanded generating
set. In this article we give a simple formula that computes the
reflection length of any element in any affine Coxeter group. In the affine symmetric group, we have a combinatorial formula that generalizes D\'enes' formula for reflection length in the symmetric group.
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
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