An enumeration of distinct and non-isomorphic functional quasi-order relations

Abstract

The problem of enumerating the number of distinct functional quasi-orders and the number of non-isomorphic functional quasi-orders that can be formed from a finite point set is considered. We establish the link between functional quasi-orders, functional digraphs, and functional Alexandroff topologies. As a result, we provide the generating functions associated to orbit-equivalent and orbit-isomorphic functional digraphs.