Periodicity in Rectangular Arrays
Discrete Mathematics
2016-07-04 v2 Combinatorics
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.
Cite
@article{arxiv.1602.06915,
title = {Periodicity in Rectangular Arrays},
author = {Guilhem Gamard and Gwenaël Richomme and Jeffrey Shallit and Taylor J. Smith},
journal= {arXiv preprint arXiv:1602.06915},
year = {2016}
}