Coverability in Two Dimensions

Guilhem Gamard (1) , Gwenaël Richomme (1, 2)

1 ESCAPE - Systèmes complexes, automates et pavages
2 UPVM - Université Paul-Valéry - Montpellier 3

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.

Mots clés: Two dimension words; Combinatorics on Words; Quasiperiodic

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Guilhem Gamard, Gwenaël Richomme. Coverability in Two Dimensions. 9th International Conference on Language and Automata Theory and Applications (LATA), Mar 2015, Nice, France. pp.402-413, ⟨10.1007/978-3-319-15579-1_31⟩. ⟨lirmm-01180026⟩