Given an ordered alphabet and
a permutation, according to the lexicographic order,
on the set of suffixes of a word
we present in this article a linear time and space method to
determine whether a word
w' has the same permutation on its suffixes.
Using this method, we are then also able to build the class of all the
words having the same permutation on their suffixes, first of all the smallest one.
Finally, we note that this work can lead to a method for generating
a Lyndon word randomly in linear time or for computing
the set of Lyndon words of length