Inequalities characterizing standard Sturmian and episturmian words

Authors:
Giuseppe Pirillo
Affiliations:
IASI, Unità di Firenze, Dipartimento di Matematica "U. Dini", Firenze, Italia and Université de Marne-la-Vallée, Marne-la-Vallée Cedex, France
Venue:
Theoretical Computer Science
Year:
2005

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Abstract

Considering the smallest and the greatest factors with respect to the lexicographic order we associate to each infinite word r two other infinite words min(r) and max(r). In this paper we prove that the inequalities as ≤ min(s) ≤ max(s) ≤ bs characterize standard Sturmian words (proper ones and periodic ones) and that the condition "for any x ∈ A and lexicographic order x = min(A) one has xs ≤ min(s)" characterizes standard episturmian words.