Counting extensional acyclic digraphs

Transitive sets with n elements were counted by Peddicord in 1962, by the use of Ackermannʼs numeric encoding of a (hereditarily finite) set. In this paper we give a combinatorial interpretation of this number by counting extensional acyclic digraphs. In a similar constructive manner, we also obtain the number of weakly extensional acyclic digraphs with a given number of labeled sinks and a given number of sources, or with a given number of vertices of maximum rank.

► Counting transitive sets is equivalent to counting extensional acyclic digraphs.
► We give a recurrence formula for labeled extensional acyclic digraphs.
► We count (weakly) extensional acyclic digraphs by sources.
► We also count (weakly) extensional acyclic digraphs by vertices of maximum rank.