Séminaire Lotharingien de Combinatoire, 82B.92 (2019), 12 pp.

Theo Douvropoulos

On enumerating factorizations in reflection groups

Abstract. We describe an approach, via Malle's permutation Ψ on the set of irreducible characters Irr(W), that gives a uniform derivation of the Chapuy-Stump formula for the enumeration of reflection factorizations of the Coxeter element. It also recovers its weighted generalization by delMas, Reiner, and Hameister, and further produces structural results for factorization formulas of arbitrary regular elements.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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