On the Triangle Conjecture
In the following N denotes the set of nonnegative integers, A = {a, b} a two-letters alphabet and A* the free monoid of base A. An element w of A* is called a word and ]w] denotes its length. A subset X of A* is a code over A if X is the base of the free submonoid X* of A*, i.e., if any work of X*\ 1 has a unique factorization in terms of the elements of X. It has been conjectured by Perrin and Schtitzenberger as follows (see [3]).