On a problem of walks
In 1995, F. Jaeger and M.-C. Heydemann began to work on a conjecture on binary operations which are related to homomorphisms of De Bruijn digraphs. For this, they have considered the class of digraphs such that for any integer , has exactly walks of length , where is the order of . Recently, C. Delorme has obtained some results on the original conjecture. The aim of this paper is to recall the conjecture and to report where all the authors arrived.