Alladi Ramakrishnan Hall

The cycle index for groups of matrices

Amritanshu Prasad

IMSc

In analogy with the Polya cycle index for group actions on finite sets, Kung defined a cycle index for linear actions of groups on a vector space.

A generating function for this cycle index allows us to give generating functions for many combinatorial functions associated to matrices over finite fields.

I will explain this technique along with some examples, and also indicate how it can be used to count representations of quivers.