Characterizations of finite and infinite episturmian words via lexicographic orderings

Details Characterizations of finite and infinite episturmian words via lexicographic orderings Characterizations of finite and infinite episturmian words via lexicographic orderings

2007-08-31

arxiv.org/abs/0708.4409v1

European Journal of Combinatorics 29 (2008) 45-58

Mathematics

Combinatorics

18 pages; to appear in the European Journal of Combinatorics

Scientific paper

10.1016/j.ejc.2007.01.002

In this paper, 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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