Some New Integer Sequences of Transitive Relations
Firdous Ahmad Mala · Journal of Applied Mathematics and Computation · 2023
Enumerative Combinatorics is the study of methods and problems related to enumeration or counting objects of various finite sets. Among several open problems in enumerative combinatorics is the problem of counting transitive relations on a set. In this paper, we discuss three problems closely related to the open problem of counting transitive relations on a finite set. These are the problems of counting the number of transitive but not symmetric relations on a set, that of counting transitive relations involving all the elements of a finite set, and that of counting transitive relations that involve a specific element of a set. We highlight the inclusion of three new sequences to the Online Encyclopedia of Integer Sequences (OEIS) that correspond to these special kinds of transitive relations. We also tabulate the first seventeen terms of each of these three sequences. The paper can be viewed as a demonstration also. The ideas demonstrated in this paper can be used as instances for giving rise to more related combinatorial problems from a given problem.