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The main goal of this work is to establish a bijection between Dyck words anda family of Eulerian digraphs. We do so by providing two algorithmsimplementing such bijection in both directions. The connection between Dyckwords and Eulerian digraphs exploits a novel combinatorial structure: a binarymatrix, we call Dyck matrix, representing the cycles of an Eulerian digraph.

Eulerian digraphs and Dyck words, a bijection