Abstract
Let R be a commutative ring with identity. Let X be a vector sequence in \(\mathfrak{M}: = {R^t}\), such that X (m) ∑ k h =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.
The authors were partially supported by the Italian M.U.R.S.T.
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References
Cerruti, U. and Vaccarino, F. “Matrices, Recurrent Sequences and Arithmetic”, in this volume.
Singh, S. “Recurring Sequences over Vector Spaces”. Lin. Alg. Appl. Vol. 131, (1990): pp. 93–106.
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© 1996 Kluwer Academic Publishers
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Cerruti, U., Vaccarino, F. (1996). Vector Linear Recurrence Sequences in Commutative Rings. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0223-7_6
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DOI: https://doi.org/10.1007/978-94-009-0223-7_6
Publisher Name: Springer, Dordrecht
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