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We prove that if a uniformly recurrent infinite word contains as a factor anyfinite permutation of words from an infinite family, then either this word isperiodic, or its complexity (that is, the number of factors) grows faster thanlinearly. This result generalizes one of the lemmas of a recent paper by deLuca and Zamboni, where it was proved that such an infinite word cannot beSturmian.

Words containing all permutations of a family of factors