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On the Number of Structures of Reflexive and Transitive Relations

Published online by Cambridge University Press:  20 November 2018

K. A. Broughan
K. A. Broughan*
Affiliation:
University of Waikato, Hamilton, New Zealand
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If for each permutation the number of partial orderings fixed by that permutation is known, it is possible to count the number of non-isomorphic partial orderings on a finite set using a lemma of Burnside. In this paper it is shown that knowledge of the numbers of partial orderings fixed by permutations will enable the number of non-isomorphic pre-orderings to be counted also.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 6 , December 1973 , pp. 1269 - 1273
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Davis, R. L., The number of structures of finite relations, Proc. Amer. Math. Soc. 4 (1953), 486–495.Google Scholar
2. Gupta, H., The number of topologies on a finite set, Research Bulletin (N.S.) of the Panjab Univ. 19, parts I-II (1968), 231–241.Google Scholar
3. Broughan, K. A., Shrinking finite topologies (to appear in Math. Chronicle).Google Scholar