Let k >= 2 be an integer. A sequence of natural numbers is k-synchronized if its graph is represented, in base k, by a right-synchronized rational relation. We show that the factor complexity and the palindromic complexity of a k-synchronized sequence are k-regular sequences. We derive that the palindromic complexity of a k-automatic sequence is k-automatic.
On factors of synchronized sequences
CARPI, Arturo;
2010
Abstract
Let k >= 2 be an integer. A sequence of natural numbers is k-synchronized if its graph is represented, in base k, by a right-synchronized rational relation. We show that the factor complexity and the palindromic complexity of a k-synchronized sequence are k-regular sequences. We derive that the palindromic complexity of a k-automatic sequence is k-automatic.File in questo prodotto:
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