Counting Quasi-idempotent Irreducible Integral Matrices
E. Thörnblad and J. Zimmermann
Department of Mathematics
Uppsala University
Box 480
751 06 Uppsala
Sweden
Abstract:
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
generalized partitions.
Full version: pdf,
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(Concerned with sequences
A006171
A129921
A280782
A280783.)
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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