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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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