Missouri Journal of Mathematical Sciences

Jordan Forms and $n$th Order Linear Recurrences

Thomas McKenzie, Shannon Overbay, and Robert Ray

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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.

Article information

Source
Missouri J. Math. Sci., Volume 26, Issue 2 (2014), 122-133.

Dates
First available in Project Euclid: 18 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1418931954

Digital Object Identifier
doi:10.35834/mjms/1418931954

Mathematical Reviews number (MathSciNet)
MR3293810

Zentralblatt MATH identifier
1352.11026

Subjects
Primary: 11B50: Sequences (mod $m$)

Keywords
matrix groups linear recurrences over $Z_p$

Citation

McKenzie, Thomas; Overbay, Shannon; Ray, Robert. Jordan Forms and $n$th Order Linear Recurrences. Missouri J. Math. Sci. 26 (2014), no. 2, 122--133. doi:10.35834/mjms/1418931954. https://projecteuclid.org/euclid.mjms/1418931954


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