On Periodicity of Generalized Pseudostandard Words

Abstract

Generalized pseudostandard words were introduced by de Luca and De Luca in [9]. In comparison to the palindromic and pseudopalindromic closure, only little is known about the generalized pseudopalindromic closure and the associated generalized pseudostandard words. We present a counterexample to Conjecture 43 from a paper by Blondin Massé et al.[2] that estimated the complexity of binary generalized pseudostandard words as C(n) ≤ 4n for all sufficiently large n. We conjecture that C(n) < 6n for all n ∈ N. : 16 (2016) INTEGERS