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Pinnacles for complex reflection groups
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DOI：10.1016/j.disc.2026.115222.png)
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Abstract
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We study, characterize, and enumerate the admissible pinnacle sets of nonexceptional complex reflection groups G(m,p,n), which include all generalized symmetric groups Z(m) (sic) S-n as special cases. This generalizes the work of Davis-Nelson-Petersen-Tenner for symmetric groups Snand Gonzalez-Harris-Rojas Kirby-Smit Vega Garcia-Tenner for signed symmetric groups Z(2) (sic) S-n. As a consequence, we prove a conjecture of Gonzalez-Harris-Rojas Kirby-Smit Vega Garcia-Tenner for pinnacles of signed permutations. (c) 2026 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Keywords:
Enumeration of permutation statistics
Pinnacle sets
Complex reflection groups
Generalized symmetric group
Peak sets
Journal
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285
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