A classic result of Hurwitz, often credited to Denes, says that in the symmetric group on n letters, there are n^{n-2} ways to factor an n-cycle into n-1 transpositions. Recent joint work with J. Lewis and D. Stanton (arXiv: arXiv:1308.1468) uncovered a finite field q-analogue: in the general linear group GL_n(F_q), there are (q^n-1)^{n-1} ways to factor a Singer cycle into n reflections. This talk will discuss what this means, and how to prove such things.
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