Author

Patrick Wegener

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Preprint Sep 2026

Hurwitz Equivalence of Reflection Factorizations in Types $B$ and $D$

A conjecture of Lewis asserts that two reflection factorizations of the same element in a finite Coxeter group $W$ belong to the same Hurwitz orbit if and only if they generate the same subgroup $H$ of $W$ and have the same multiset of $H$-conjugacy classes. We prove this conjecture for every finite Coxeter group all o...

Patrick Wegener · 0 citations

Preprint Sep 2026

Commutators of signed $n$-cycles

We show that for $n \geq 6$ each element of the commutator subgroup in the symmetric group $\mathfrak{S}_n$ resp. in the signed symmetric group $(\mathbb{Z}/2\mathbb{Z})^n\rtimes\mathfrak{S}_n$ is the commutator of two $n$-cycles resp. the commutator of two $n$-cycles with a negative sign product; with one exception. I...

P. Bader, Bernhard Böhmler, Patrick Wegener · 0 citations