Subword Complexity and k-Synchronization

Daniel Goc; Luke Schaeffer; Jeffrey Shallit

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arXiv · 1206.5352

Subword Complexity and k-Synchronization

Daniel Goc·Luke Schaeffer·Jeffrey Shallit

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Abstract

We show that the subword complexity function p_x(n), which counts the number of distinct factors of length n of a sequence x, is k-synchronized in the sense of Carpi if x is k-automatic. As an application, we generalize recent results of Goldstein. We give analogous results for the number of distinct factors of length n that are primitive words or powers. In contrast, we show that the function that counts the number of unbordered factors of length n is not necessarily k-synchronized for k-automatic sequences.

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Daniel Goc, Luke Schaeffer, Jeffrey Shallit. 2012-06-23. Subword Complexity and k-Synchronization. https://arxiv.org/abs/1206.5352

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