Journal of Integer Sequences, Vol. 21 (2018), Article 18.4.8

Counting Quasi-idempotent Irreducible Integral Matrices

E. Thörnblad and J. Zimmermann
Department of Mathematics
Uppsala University
Box 480
751 06 Uppsala


Given any polynomial pC[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.

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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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