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?A and lexicographic order < satisfying x=min(A) one has xs<=min(s)" characterizes standard episturmian words. © 2005 Elsevier B.V. All rights reserved.