The number of regular semisimple conjugacy classes in the finite classical groups

TL;DR

This paper uses generating functions to count regular semisimple conjugacy classes in finite classical groups, providing new results for special orthogonal groups and alternative proofs for others.

Contribution

It introduces a novel generating function approach to enumerate regular semisimple conjugacy classes, offering new results for special orthogonal groups and alternative methods for general linear, unitary, and symplectic groups.

Findings

Counts conjugacy classes in finite classical groups

Provides new enumeration results for special orthogonal groups

Offers alternative proofs for known results in other groups

Abstract

Using generating functions, we enumerate regular semisimple conjugacy classes in the finite classical groups. For the general linear, unitary, and symplectic groups this gives a different approach to known results; for the special orthogonal groups the results are new.