Periodicity in Rectangular Arrays
  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. 
Guilhem Gamard, Gwena\"el Richomme, Jeffrey Shallit, Taylor J. Smith
cs.DM math.CO