Factoring cycles | Department of Mathematics

Factoring cycles

Event Information
Event Location: 
GAB 461, 4-5 PM; Refreshments: GAB 472, 3:30 PM
Event Date: 
Monday, March 17, 2014 - 4:00pm

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.