Asymptotic Analysis of q-Recursive Sequences

A Note on the Relation between Recognisable Series and Regular Sequences, and their Minimal Linear Representations

“…Such an error occurred while preparing the SageMath [6] implementation of q-recursive sequences with inhomogeneities (cf. [5]) for [4] and motivated the authors to precisely investigate the situation. The main result of this note is that as long as the linear representation of a regular sequence is "proper" in the above sense, using the minimisation algorithm for recognisable series yields the expected result.…”