Conjugacy-class generating function for finite general linear groups
= Conjugacy-class generating function for finite general linear groups
If $k_n(q)$ counts <conjugacy classes> in $GL_n(q)$, then $\sum_{n\ge0}k_n(q)t^n=\prod_{i\ge1}(1-t^i)/(1-qt^i)$. Associate a partition to each irreducible polynomial other than t. The Euler product over those polynomials counts monic polynomials with nonzero constant term and is $(1-u)/(1-qu)$.