Why the number of transitive relations is not an integer polynomial

Abstract

The age-old problem of enumerating all relations on a set that are transitive is still unsolved. Despite numerous
attempts in this direction, the number of transitive relations for a set is known only for sets with fewer than nineteen
elements. In a recent article, it was shown that the count of transitive relations on n nodes is not a polynomial. In
this article, an alternative intuitive proof of this fact is presented.