A079265 Number of antisymmetric transitive binary relations on n unlabeled points.

1, 2, 7, 32, 192, 1490, 15067, 198296, 3398105, 75734592, 2191591226, 82178300654, 3984499220967, 249298391641352, 20089200308020179, 2081351202770089728

Offset: 0

Author

N. J. A. Sloane, Feb 16 2003

Keywords

• nonn
• hard
• nice

Comments

Also, number of unconstrained mixed models with n factors.

References

• 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.

Links

• 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 progrès dans l'énumération des modèles mixtes, in Knowledge discovery and discrete mathematics : JIM'2003, INRIA, Université de Metz, France, 2003, pp. 243-246.
• Gunnar Brinkmann and Brendan D. McKay, Counting unlabelled topologies and transitive relations.
• Gunnar Brinkmann and Brendan D. McKay, Counting Unlabelled Topologies and Transitive Relations, Journal of Integer Sequences, Vol. 8 (2005), Article 05.2.1.
• R. Fraïssé and N. Lygeros, Petits posets: dénombrement, représentabilité par cercles et "compenseurs", C. R. Acad. Sci. Paris, Vol. 313, series I, pp. 417-420, 1991.
• 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.

Crossrefs

Cf. A000112 (partial orders), A091073 (transitive relations), A001930 (quasi-orders), A085628 (labeled antisymmetric transitive relations).

Cf. A079263, A006126, A006602, A006896-A006898.

Extensions

a(10)-a(12) and new description from Goetz Pfeiffer (goetz.pfeiffer(AT)nuigalway.ie), Jan 21 2004

a(13)-a(15) from Brinkmann's and McKay's paper by Vladeta Jovovic, Jan 04 2006