# An inequality for the number of periods in a word

@article{Gabric2021AnIF, title={An inequality for the number of periods in a word}, author={Daniel Gabric and Narad Rampersad and Jeffrey Shallit}, journal={Int. J. Found. Comput. Sci.}, year={2021}, volume={32}, pages={597-614} }

We prove an inequality for the number of periods in a word x in terms of the length of x and its initial critical exponent. Next, we characterize all periods of the length-n prefix of a characteristic Sturmian word in terms of the lazy Ostrowski representation of n, and use this result to show that our inequality is tight for infinitely many words x. We propose two related measures of periodicity for infinite words. Finally, we also consider special cases where x is overlap-free or squarefree.

## 2 Citations

On the conjugates of Christoffel words

- Mathematics
- 2022

We introduce a parametrization of the conjugates of Christoffel words based on the integer Ostrowski numeration system. We use it to give a precise description of the borders (prefixes which are also…

Decidability for Sturmian words

- MathematicsCSL
- 2022

It is proved that the first-order expansions of Presburger arithmetic by a single Sturmian word are uniformly ω-automatic, and the decidability of the theory of the class of such structures is deduced.

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