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math.CO2022★ 7 cited
Hurwitz numbers for reflection groups II: Parabolic quasi-Coxeter elements
Theo Douvropoulos, Joel Brewster Lewis, Alejandro H. Morales
We define parabolic quasi-Coxeter elements in well generated complex reflection groups. We characterize them in multiple natural ways, and we study two combinatorial objects associ…
math.CO2022
In which it is proven that, for each parabolic quasi-Coxeter element in a finite real reflection group, the orbits of the Hurwitz action on its reflection factorizations are distinguished by the two obvious invariants
Theo Douvropoulos, Joel Brewster Lewis
We prove that two reflection factorizations of a parabolic quasi-Coxeter element in a finite Coxeter group belong to the same Hurwitz orbit if and only if they generate the same su…
math.PR2022
A Random Card Shuffling Process
Joel Brewster Lewis, Mehr Rai
Consider a randomly shuffled deck of cards with red cards and black cards. We study the average number of moves it takes to go from a randomly shuffled deck to a deck…