Hurwitz Orbits of Equal Size
Combinatorics
2022-09-05 v1 Group Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2102.01145,
title = {Hurwitz Orbits of Equal Size},
author = {Colin Pirillo and Seth Sabar},
journal= {arXiv preprint arXiv:2102.01145},
year = {2022}
}
Comments
14 pages