Cycle index series of structures over digraphs Original Research Article

Recently, we introduced (Méndez, Adv. Math. 123 (1996) 243–275.) a generalization of Joyal (Adv. Math. 42 (1981) 1–82) species in order to enumerate structures constructed over arc-labeled directed graphs (species on digraphs). We introduce here the Z-series for species on digraphs, in analogy with Joyal Z-series for ordinary species. We apply the Z-series to obtain classical and new generating functions for unlabeled structures on digraphs.