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arXiv · 1602.06915

Periodicity in Rectangular Arrays

Guilhem Gamard·Gwenaël Richomme·Jeffrey Shallit·Taylor J. Smith
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Abstract

We discuss several two-dimensional generalizations of the familiar Lyndon-Schutzenberger periodicity theorem for words. We consider the notion of primitive array (as one that cannot be expressed as the repetition of smaller arrays). We count the number of m x n arrays that are primitive. Finally, we show that one can test primitivity and compute the primitive root of an array in linear time.

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Guilhem Gamard, Gwenaël Richomme, Jeffrey Shallit, Taylor J. Smith. 2016-02-22. Periodicity in Rectangular Arrays. https://arxiv.org/abs/1602.06915

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