The number of shortest factorizations into reflections for a Singer cycle in GLn(Fq) is shown to be (qn - 1)n-1. Formulas counting factorizations of any length, and counting those with reflections of fixed conjugacy classes are also given.
|Original language||English (US)|
|Number of pages||12|
|Journal||Discrete Mathematics and Theoretical Computer Science|
|State||Published - 2014|
|Event||26th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2014 - Chicago, United States|
Duration: Jun 29 2014 → Jul 3 2014
Bibliographical noteFunding Information:
Work partially supported by NSF grants DMS-1148634 and DMS-1001933.
- Anisotropic maximal torus
- Coxeter element
- Coxeter torus
- Finite general linear group
- Higher genus
- Regular element
- Singer cycle