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On the enumeration of homeomorphism classes of finite topologies

Published online by Cambridge University Press:  09 April 2009

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

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An algorithm called UNLABEL is devised to uniquely label an unlabelled transitive digraph. This is used to construct a one-one correspondence between homeomorphism classes of finite nondiscrete To-topologies and certain generalised Young tableaux of shape-type α. For sets of cardinality 2, 3, 4 and 5 these classes are enumerated and classified in several ways. The notion of a generalised descriptor graph is then introduced to enumerate the homeomorphism classes of all topologies on these sets.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 3 , November 1977 , pp. 320 - 338
Copyright
Copyright © Australian Mathematical Society 1977

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