Pseudoperiodic words

Abstract

We consider words over an arbitrary alphabet admitting two pseudoperiods: a σ 1-period and a σ 2-period, where σ 1 and σ 2 are permutations. We describe the conditions under which such a word exists. Moreover, a natural generalization of Fine and Wilf's Theorem is proved. Finally, we introduce and describe a new family of words sharing properties with the so-called central words. In particular, under some simple conditions, we prove that these words are pseudopalindromes, a result consistent with the fact that central words are palindromes. © 2012 Springer-Verlag.