Counting extensional acyclic digraphs

Authors:
Alberto Policriti;Alexandru I. Tomescu
Affiliations:
Dipartimento di Matematica e Informatica, Universití di Udine, Via delle Scienze, 206, 33100 Udine, Italy;Dipartimento di Matematica e Informatica, Universití di Udine, Via delle Scienze, 206, 33100 Udine, Italy and Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academ ...
Venue:
Information Processing Letters
Year:
2011

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Abstract

Transitive sets with n elements were counted by Peddicord in 1962, by the use of Ackermann@?s 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.