J.B. Lewis ; V. Reiner ; D. Stanton
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Reflection factorizations of Singer cycles
dmtcs:2401 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2014,
DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
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https://doi.org/10.46298/dmtcs.2401
Reflection factorizations of Singer cycles
Authors: J.B. Lewis 1; V. Reiner 1; D. Stanton 1
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J.B. Lewis;V. Reiner;D. Stanton
1 School of Mathematics
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.