Coverability in two dimensions

Abstract

A word is quasiperiodic (or coverable) if it can be covered by occurrences of another finite word, called its quasiperiod. This notion was previously studied in the domains of text algorithms and combinatorics of right infinite words. We extend several results to two dimensions. We also characterize all rectangular words that cover non-periodic two-dimensional infinite words. Then we focus on two-dimensional words with infinitely many quasiperiods. We show that such words have zero entropy. However, contrarily to the one-dimensional case, they may not be uniformly recurrent.