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arXiv · 2510.03580

Pinnacles for Complex Reflection Groups

Aaron Burnham-Schmidt·Nicolle González
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Abstract

We study, characterize, and enumerate the admissible pinnacle sets of nonexceptional complex reflection groups $G(m,p,n)$, which include all generalized symmetric groups $\mathbb{Z}_m \wr S_n$ as special cases. This generalizes the work of Davis--Nelson--Petersen--Tenner for symmetric groups $S_n$ and González--Harris--Rojas Kirby--Smit Vega Garcia--Tenner for signed symmetric groups $\mathbb{Z}_2 \wr S_n$. As a consequence, we prove a conjecture of González--Harris--Rojas Kirby--Smit Vega Garcia--Tenner for pinnacles of signed permutations.

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Aaron Burnham-Schmidt, Nicolle González. 2025-10-04. Pinnacles for Complex Reflection Groups. https://arxiv.org/abs/2510.03580

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