Pinnacles for Complex Reflection Groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911191225335808 |
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| author | Burnham-Schmidt, Aaron González, Nicolle |
| author_facet | Burnham-Schmidt, Aaron González, Nicolle |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03580 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pinnacles for Complex Reflection Groups Burnham-Schmidt, Aaron González, Nicolle Combinatorics 05A05, 05A15, 05E16 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. |
| title | Pinnacles for Complex Reflection Groups |
| topic | Combinatorics 05A05, 05A15, 05E16 |
| url | https://arxiv.org/abs/2510.03580 |