Pinnacles for Complex Reflection Groups

We study, characterize, and enumerate the admissible pinnacle sets of nonexceptional complex reflection groups $G(m,p,n)$, which include all generalized symmetric groups Zₘ Sₙ as special cases. This generalizes the work of Davis--Nelson--Petersen--Tenner for symmetric groups Sₙ and González--Harris--Rojas Kirby--Smit Vega Garcia--Tenner for signed symmetric groups Z₂ Sₙ. As a consequence, we prove a conjecture of González--Harris--Rojas Kirby--Smit Vega Garcia--Tenner for pinnacles of signed permutations.