Characterizations of finite and infinite episturmian words via lexicographic orderings

   Amy Glen (CRM-ISM-LaCIM, UQAM)

Abstract: In this talk, I will present some new results arising from collaborative work with Jacques Justin (France) and Giuseppe Pirillo (Italy). This work, which extends previous results on extremal properties of infinite Sturmian and episturmian words, is purely combinatorial in nature. Specifically, we characterize by lexicographic order all finite Sturmian and episturmian words, i.e., all (finite) factors of such infinite words. Consequently, we obtain a characterization of infinite episturmian words in a wide sense (episturmian and episkew infinite words). That is, we characterize the set of all infinite words whose factors are (finite) episturmian. Similarly, we characterize by lexicographic order all balanced infinite words over a 2-letter alphabet; in other words, all Sturmian and skew infinite words, the factors of which are (finite) Sturmian.

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