ALGEBRAIC COMBINATORICS

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

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.

Received:
Revised:
Accepted:
Published online:
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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Douvropoulos, Theo. On enumerating factorizations in reflection groups. Algebraic Combinatorics, Volume 6 (2023) no. 2, pp. 359-385. doi : 10.5802/alco.261. https://alco.centre-mersenne.org/articles/10.5802/alco.261/

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