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A079265
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Number of antisymmetric transitive binary relations on n unlabeled points.
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5
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1, 2, 7, 32, 192, 1490, 15067, 198296, 3398105, 75734592, 2191591226, 82178300654, 3984499220967, 249298391641352, 20089200308020179, 2081351202770089728
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OFFSET
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0,2
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COMMENTS
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Also, number of unconstrained mixed models with n factors.
[ a(13)-a(15) are from Brinkmann's and McKay's paper ] - Vladeta Jovovic, Jan 04 2006
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REFERENCES
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Gunnar Brinkmann and Brendan D. McKay, Counting Unlabeled Topologies and Transitive Relations, Journal of Integer Sequences, Vol. 8 (2005), Article 05.2.1.
A. Hess and H. Iyer, Enumeration of mixed linear models and SAS macro for computation of confidence intervals for variance components, presented at Applied Statistics in Agriculture Conference at Kansas State University 2001. See also C. R. Acad. Sci. Paris, Vol. 313, series I, pp. 417-420, 1991.
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LINKS
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Table of n, a(n) for n=0..15.
R. Bayon, N. Lygeros and J.-S. Sereni, New progress in enumeration of mixed models, Applied Mathematics E-Notes, 5 (2005), 60-65.
R. Bayon, N. Lygeros and J.-S. Sereni, Nouveaux progr\`es dans l'\'enum\'eration des mod\`eles mixtes, in Knowledge discovery and discrete mathematics : JIM'2003, INRIA, Universit\'e de Metz, France, 2003, pp. 243-246.
Gunnar Brinkmann and Brendan D. McKay, Counting unlabeld topologies and transitive relations.
Ann Marie Hess, Mixed Models Site
G. Pfeiffer, Counting Transitive Relations, preprint, 2004.
G. Pfeiffer, Counting Transitive Relations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.2.
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CROSSREFS
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Cf. A000112 (partial orders), A091073 (transitive relations), A001930 (quasi-orders), A085628 (labeled antisymmetric transitive relations).
Cf. A079263, A006126, A006602, A006896-A006898.
Sequence in context: A006957 A189780 A195983 * A112006 A067551 A080119
Adjacent sequences: A079262 A079263 A079264 * A079266 A079267 A079268
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KEYWORD
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nonn,hard,nice
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AUTHOR
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N. J. A. Sloane, Feb 16 2003
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EXTENSIONS
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New description and a(10)-a(12) from Goetz Pfeiffer (goetz.pfeiffer(AT)nuigalway.ie), Jan 21 2004
More terms from Vladeta Jovovic, Jan 04 2006
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STATUS
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approved
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