Vector Linear Recurrence Sequences in Commutative Rings

Umberto Cerruti and Francesco Vaccarino

A chapter in Applications of Fibonacci Numbers, 1996, pp 63-72 from Springer

Abstract: Abstract Let R be a commutative ring with identity. Let X be a vector sequence in $$\mathfrak{M}: = {R^t}$$ , such that X (m) ∑ h k =1 X (m−h) G h , with G h € Mat(t,R). The main result of this paper is to show that X can be computed as a linear recurrence sequence (in $$\mathfrak{M}$$ ) with scalar coefficients.

Date: 1996
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DOI: 10.1007/978-94-009-0223-7_6

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