Alladi Ramakrishnan Hall

Asymptotic for Counting Similarity Classes of Tuples of Commuting Matrices

Uday Bhaskar Sharma

IMSc

Let c(n,k,q) be the number of similarity classes of commuting k-tuples of nxn matrices with entries in a finite field with q elements. We will show that c(n,k,q) is asymptotically q^(([n^2/4]+1)k) as a function of k.