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.