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Asymptotic enumeration of partial orders on a finite set. (English) Zbl 0302.05007

MSC:
05A15 Exact enumeration problems, generating functions
06A06 Partial orders, general
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[1] K. K.-H. Butler, The number of finite partially ordered sets, Notices Amer. Math. Soc. 18 (1971), 1092. Abstract #71T-A250.
[2] S. D. Chatterji, The number of topologies on \( n\) points, Kent State University, NASA Technical Report, 1966.
[3] Louis Comtet, Recouvrements, bases de filtre et topologies d’un ensemble fini, C. R. Acad. Sci. Paris Sér. A-B 262 (1966), A1091 – A1094 (French). · Zbl 0152.39701
[4] J. W. Evans, F. Harary and M. S. Lynn, On the computer enumeration of finite topologies, Comm. ACM 10 (1967), 295-298. · Zbl 0166.01003
[5] David A. Klarner, The number of graded partially ordered sets, J. Combinatorial Theory 6 (1969), 12 – 19. · Zbl 0169.32401
[6] David A. Klarner, The number of classes of isomorphic graded partially ordered sets, J. Combinatorial Theory 9 (1970), 412 – 419. · Zbl 0177.02301
[7] D. Kleitman and B. Rothschild, The number of finite topologies, Proc. Amer. Math. Soc. 25 (1970), 276 – 282. · Zbl 0197.18802
[8] V. Krishnamurthy, On the number of topologies on a finite set, Amer. Math. Monthly 73 (1966), 154 – 157. · Zbl 0135.40704 · doi:10.2307/2313548 · doi.org
[9] A. Shafaat, On the number of topologies definable for a finite set, J. Austral. Math. Soc. 8 (1968), 194 – 198. · Zbl 0153.52101
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