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Journal Articles Information Processing Letters Year : 2017

Periodicity in rectangular arrays

Abstract

We discuss several two-dimensional generalizations of the familiar Lyndon–Schützenberger 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 mxn arrays that are primitive. Finally, we show that one can test primitivity and compute the primitive root of an array in linear time.

Dates and versions

lirmm-01378894 , version 1 (10-10-2016)

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Guilhem Gamard, Gwenaël Richomme, Jeffrey Shallit, Taylor J. Smith. Periodicity in rectangular arrays. Information Processing Letters, 2017, 118, pp.58-63. ⟨10.1016/j.ipl.2016.09.011⟩. ⟨lirmm-01378894⟩
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