Eulerian digraphs and Dyck words, a bijection
  The main goal of this work is to establish a bijection between Dyck words and a family of Eulerian digraphs. We do so by providing two algorithms implementing such bijection in both directions. The connection between Dyck words and Eulerian digraphs exploits a novel combinatorial structure: a binary matrix, we call Dyck matrix, representing the cycles of an Eulerian digraph. 
Pietro Codara, Ottavio M. D'Antona, Marco Genuzio
cs.DM math.CO