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.
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Dasre, N.R., Gujarathi, P.: Topologies on finite sets. Int. J. Pure Appl. Math. 118(1), 39–48 (2018)
Sloane, N.J.A.: Online encyclopedia of integer sequences. http://oeis.org/A001035/list
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Dasre, N.R., Gujarathi, P. (2020). Approximating the Bounds for Number of Partially Ordered Sets with n Labeled Elements. In: Iyer, B., Deshpande, P., Sharma, S., Shiurkar, U. (eds) Computing in Engineering and Technology. Advances in Intelligent Systems and Computing, vol 1025. Springer, Singapore. https://doi.org/10.1007/978-981-32-9515-5_33
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DOI: https://doi.org/10.1007/978-981-32-9515-5_33
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