Automatic sequences and formal algebraic series : q-Core of a sequence, Cartier q-operators, a first theorem

q-Core of a sequence, Cartier q-operators, a first theorem
Automatic sequences and formal algebraic series

Author : Jean-Paul ALLOUCHE

Publication date: October 10, 2005 | Lire en français

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3. q-Core of a sequence, Cartier q-operators, a first theorem

Definition 10. Let $a : = {(a_{n})}_{n \geq 0}$ be a sequence defined on an alphabet $A$ and let q be an integer $\geq 2$ .

We call the q-kernel of the sequence a and note N _a the set of sub-suites

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q-Core of a sequence, Cartier q-operators, a first theorem

(1) - ALLOUCHE (J.-P.), SHALLIT (J.) - Automatic sequences. Theory, Applications, Generalizations - , Cambridge University Press, 571 + xvi pages (2003).
(2) - CHRISTOL (G.) - Ensembles presque périodiques k-reconnaissables - , Theoretical Computer Science...

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