Reflection factorizations of Singer cycles
oleh: J.B. Lewis, V. Reiner, D. Stanton
| Format: | Article |
|---|---|
| Diterbitkan: | Discrete Mathematics & Theoretical Computer Science 2014-01-01 |
Deskripsi
The number of shortest factorizations into reflections for a Singer cycle in $GL_n(\mathbb{F}_q)$ is shown to be $(q^n-1)^{n-1}$. Formulas counting factorizations of any length, and counting those with reflections of fixed conjugacy classes are also given.