Hurwitz Orbits of Equal Size

  • Colin Pirillo Yale University
  • Seth Sabar Brown University
Keywords: Hurwitz action; Hurwitz orbit; factorizations of elements in groups; complex reflection groups; Coxeter groups; Shephard groups


We provide a variety of cases in which two factorizations have Hurwitz orbits of the same size. We begin with prototypical results about factorizations of length two, and show that cycling elements or flipping and inverting elements in any factorization preserves Hurwitz orbit size. We prove that "double reverse" factorizations in groups with special presentations have Hurwitz orbits of equal size, and end with applications to complex reflection groups.

How to Cite
Pirillo, C., & Sabar, S. (2022). Hurwitz Orbits of Equal Size. The PUMP Journal of Undergraduate Research, 5, 52-64. Retrieved from