The number of non-isomorphic ternary relations

Abstract

In 1953, R. L. Davis succeeded in counting several different kinds of binary relations on p objects. As their natural extensions, the number of non-isomorphic (unrepeatable) unordered and ordered ternary relations are studied respectively in this paper. Moreover, as generalizations of locally restricted graphs (resp. digraphs), we introduce the definitions of locally restricted, unordered (resp. ordered) ternary relations. Furthermore, thengenerating functions are obtained, respectively.