Geodesic
On the Number of Structures of Reflexive and Transitive Relations
Canadian journal of mathematics, Tome 25 (1973) no. 6, pp. 1269-1273

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Broughan, K. A. On the Number of Structures of Reflexive and Transitive Relations. Canadian journal of mathematics, Tome 25 (1973) no. 6, pp. 1269-1273. doi: 10.4153/CJM-1973-133-9
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[1] 1. Davis, R. L., The number of structures of finite relations, Proc. Amer. Math. Soc. 4 (1953), 486–495. Google Scholar

[2] 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] 3. Broughan, K. A., Shrinking finite topologies (to appear in Math. Chronicle). Google Scholar

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