Properties of a class of Toeplitz words

We study the properties of the uncountable set of . These are Toeplitz words specified by infinite sequences of Toeplitz patterns of the form , where is any permutation of the symbols . We determine the critical exponent of the Stewart words, prove that they avoid the pattern , find all factors that are palindromes, and determine their subword complexity. An interesting aspect of our work is that we use automata-theoretic methods and a decision procedure for automata to carry out the proofs.