Journal of the Ramanujan Mathematical Society
Volume 31, Issue 4, December 2016 pp. 385–397.
Asymptotic of number of similarity classes of commuting tuples
Authors:
Uday Bhaskar Sharma
Author institution:The Institute of Mathematical Sciences, Chennai
Summary:
Let c(n, k, q) be the number of simultaneous similarity classes
of k-tuples of commuting × matrices over a finite
field of order~q. We show that, for a fixed n and q, c(n,k,
q) is asymptotically q {m(n)k} (upto some constant factor), as
a function of k, where m(n) = [n^2/4] + 1 is the maximal
dimension of a commutative subalgebra of the algebra of n×
n matrices over the finite field.
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