Palindromic closures using multiple antimorphisms

A generalized pseudostandard word u, as introduced in 2006 by de Luca and De Luca, is given by a directive sequence of letters from an alphabet AA and by a directive sequence of involutory antimorphisms acting on A⁎A⁎. Prefixes of u with increasing length are constructed using a pseudopalindromic closure operator.We show that generalized Thue–Morse words tb,mtb,m, with b,m∈Nb,m∈N and b  , m⩾2m⩾2, are generalized pseudostandard words if and only if tb,mtb,m is a periodic word or b⩽mb⩽m. This extends the result of de Luca and De Luca obtained for the classical Thue–Morse words.