Counting Quasi-idempotent Irreducible Integral Matrices
E. Thörnblad and J. Zimmermann
Department of Mathematics
751 06 Uppsala
Given any polynomial p ∈ C[X],
we show that the set of irreducible
matrices satisfying p(A) = 0 is finite.
In the specific case of the
polynomial p(X) = X2 - nX,
we count the number of irreducible matrices
in this set and analyze the resulting sequences and their asymptotics.
Such matrices turn out to be related to generalized compositions and
Full version: pdf,
(Concerned with sequences
Received February 24 2017;
revised versions received November 3 2017; April 6 2018.
Published in Journal of Integer Sequences, May 9 2018.
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