Characterizations of finite and infinite episturmian words via lexicographic orderings

Authors:
Amy Glen;Jacques Justin;Giuseppe Pirillo
Affiliations:
LaCIM, Université du Québec í Montréal, C.P. 8888, Succ. Centre-ville, Montréal, Québec, Canada, H3C 3P8;LIAFA, Université Paris VII, Case 7014, 2 place Jussieu, 75251 Paris Cedex 05, France;IASI CNR, Unití di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy
Venue:
European Journal of Combinatorics
Year:
2008

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Abstract

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.