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November 2014 Jordan Forms and $n$th Order Linear Recurrences
Thomas McKenzie, Shannon Overbay, Robert Ray
Missouri J. Math. Sci. 26(2): 122-133 (November 2014). DOI: 10.35834/mjms/1418931954

Abstract

Let $p$ be a prime number with $p\neq 2$. We consider sequences generated by $n$th order linear recurrence relations over the finite field $Z_p$. In the first part of this paper we generalize some of the ideas in [6] to $n$th order linear recurrences. We then consider the case where the characteristic polynomial of the recurrence has one root in $Z_p$ of multiplicity $n$. In this case, we show that the corresponding recurrence can be generated by a relatively simple matrix.

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Thomas McKenzie. Shannon Overbay. Robert Ray. "Jordan Forms and $n$th Order Linear Recurrences." Missouri J. Math. Sci. 26 (2) 122 - 133, November 2014. https://doi.org/10.35834/mjms/1418931954

Information

Published: November 2014
First available in Project Euclid: 18 December 2014

zbMATH: 1352.11026
MathSciNet: MR3293810
Digital Object Identifier: 10.35834/mjms/1418931954

Subjects:
Primary: 11B50

Rights: Copyright © 2014 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.26 • No. 2 • November 2014
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