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On a problem of walks

Charles Delorme; Marie-Claude Heydemann — 1999

Annales de l'institut Fourier

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 $G$ such that for any integer $k$ , $G$ has exactly $n$ walks of length $k$ , where $n$ is the order of $G$ . 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.

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