Geodesic
On enumerating factorizations in reflection groups
Douvropoulos, Theo1
1 University of Massachussets at Amherst Department of Mathematics and Statistics
Algebraic Combinatorics, Tome 6 (2023) no. 2, pp. 359-385

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

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DOI : 10.5802/alco.261
Classification : 05A15, 05E99, 20C08, 20F55
Keywords: factorization enumeration, full twist, regular elements, Frobenius lemma

Douvropoulos, Theo 1

1 University of Massachussets at Amherst Department of Mathematics and Statistics
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Douvropoulos, Theo. On enumerating factorizations in reflection groups. Algebraic Combinatorics, Tome 6 (2023) no. 2, pp. 359-385. doi: 10.5802/alco.261

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