Construction and Enumeration of a Special Class of Transitive Relations

Abstract

In this paper, we deal with the transitive relations on a finite $n$-element set. The transitive relations are interpreted as Boolean matrices. A special class of transitive relations are constructed and enumerated, which can generate all transitive
relations on a finite n-element set by intersection operation. Besides, several necessary and sufficient conditions that a relation
\(R\) is transitive are given.