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Journal of Applied Mathematics and Computation

ISSN Online: 2576-0653 ISSN Print: 2576-0645 CODEN: JAMCEZ
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ArticleOpen 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.

Keywords

Transitive Relations, Symmetric Relations, Equivalence Relations, Enumeration, Counting

References

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https://doi.org/10.1007/s13226-021-00100-0.

[8] Mala, F. A. (2021) Counting Transitive Relations with Two Ordered Pairs. Journal of Applied Mathematics and Computation, 5(4), 247-251. http://dx.doi.org/10.26855/jamc.2021.12.002.

[9] Mala, F. A. (2021). Interesting observations on the numbers of partial orders and transitive relations. Cape Comorin Trust, India, 215.

[10] DES MacHALE, and PETER MacHALE. “Relations on Sets.” The Mathematical Gazette, vol. 97, no. 539, 2013, pp. 224-33, https://doi.org/10.1017/S0025557200005817.

[11] Mala, F. A. (2023). Three Open Problems in Enumerative Combinatorics. Journal of Applied Mathematics and Computation, 7(1), 24-27. DOI: http://dx.doi.org/10.26855/jamc.2023.03.004.

[12] Mala, F. A., Gulzar, S., & Poonia, R. K. (2023, April). Inequalities concerning transitive and equivalence relations. In Advances in Pure and Applied Algebra: Proceedings of the CONIAPS XXVII International Conference 2021 (p. 3). Walter de Gruyter GmbH & Co KG. https://doi.org/10.1515/9783110785807.

Copyright

© 2023 by the author(s).
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND) license, which permits non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited and is not modified or adapted.
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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