Inequalities characterizing standard Sturmian and episturmian words
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 is an element of A and lexicographic order < satisfying x = min (A) one has xs <= min(s)" characterizes standard episturmian words. (c) 2005 Elsevier B.V. All rights reserved.
episturmian words sturmian words words lexicographic order infinite words