On a Matrix Representation for Polynomially Recursive Sequences

Christophe Reutenauer

Abstract


In this article we derive several consequences of a matricial characterization of P-recursive sequences. This characterization leads to canonical representations of these sequences. We show their uniqueness for a given sequence, up to similarity. We study their properties: operations, closed forms, d'Alembertian sequences, field extensions, positivity, extension of the sequence to $\mathbb Z$, difference Galois group.

Keywords


p-recursive; matrix representation; Galois theory

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