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Journal of Applied Mathematics and Computation

ISSN Online: 2576-0653 Downloads: 176572 Total View: 1991848
Frequency: quarterly ISSN Print: 2576-0645 CODEN: JAMCEZ
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Article Open Access http://dx.doi.org/10.26855/jamc.2023.03.011

Some New Integer Sequences of Transitive Relations

Firdous Ahmad Mala

Department of Mathematics, Government Degree College Sopore, Baramulla, Jammu and Kashmir, India.

*Corresponding author: Firdous Ahmad Mala

Published: April 20,2023

Abstract

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.

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How to cite this paper

Some New Integer Sequences of Transitive Relations

How to cite this paper:  Firdous Ahmad Mala. (2023) Some New Integer Sequences of Transitive Relations. Journal of Applied Mathematics and Computation7(1), 108-111.

DOI: http://dx.doi.org/10.26855/jamc.2023.03.011