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Counting of finite topologies and a dissection of Stirling numbers of the second kind

Published online by Cambridge University Press:  17 April 2009

V. Krishnamurthy
V. Krishnamurthy
Affiliation:
Department of Mathematics, Birla Institute of Technology and Science, Pilani (Rajasthan), India.
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Abstract

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Certain new combinatorial numbers which arise in the counting of finite topologies are introduced and formulae obtained. These numbers are used to obtain a known formula for tn, the number of labelled topologies on n points in terms of the Stirling numbers S(n, p) and dn, the number of labelled T0-topologies on n points. The numbers dn are computed for n ≤ 5 with the the help of a method of Comtet (1966) (which seems to have been missed by later authors), reinterpreted for transitive digraphs.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 1 , February 1975 , pp. 111 - 124
Copyright
Copyright © Australian Mathematical Society 1975

References

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