Language structure of pattern Sturmian words

Pattern Sturmian words introduced by Kamae and Zamboni KZ KZ are an analogy of Sturmian words for the maximal pattern com plexity instead of the block complexity So far two kinds of recur rent pattern Sturmian words are known namely rotation words and Toeplitz words But neither a structural characterization nor a reason able classi cation of the recurrent pattern Sturmian words is known In this paper we introduce a new notion pattern Sturmian sets which are used to study the language structure of pattern Sturmian words We prove that there are exactly two primitive structures for pattern Sturmian words Consequently we suggest a classi cation of pattern Sturmian words according to structures of pattern Sturmian sets and prove that there are at most three classes in this classi cation Ro tation words and Toeplitz words fall into two di erent classes but no examples of words from the third class are known