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Approximating the Bounds for Number of Partially Ordered Sets with n Labeled Elements

  • Narendrakumar R. Dasre
  • Pritam GujarathiEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1025)

Abstract

The problem of finding the number of partially ordered sets (Posets) with n labeled elements is still open for research after decades. The problem of counting number of partially ordered sets with n labeled elements arises in laying out the computer networks, wired and wireless networks. Dasre and Gujarathi [1] have introduced the idea of repeated ratios and have obtained sharper bounds for finding the number of topologies on the set with n-elements. The number of partially ordered sets with n labeled elements is same as the number of \(T_0\) topologies on a set of n elements. With the same approach in [1], we have obtained the sharper bounds for the number of partially ordered sets with n labeled elements.

Keywords

Partially ordered sets Topology Repeated ratio Lower bound Upper bound Sequence 

References

  1. 1.
    Dasre, N.R., Gujarathi, P.: Topologies on finite sets. Int. J. Pure Appl. Math. 118(1), 39–48 (2018)Google Scholar
  2. 2.
    Sloane, N.J.A.: Online encyclopedia of integer sequences. http://oeis.org/A001035/list

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Ramrao Adik Institute of TechnologyNerul, Navi MumbaiIndia

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