0,3

Also fixed effects ANOVA models with n factors, which may be both crossed and nested.

[ a(15)-a(16) are from Brinkmann's and McKay's paper ] - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 04 2006

G. Birkhoff, Lattice Theory, 1961, p. 4.

C. Chaunier and N. Lygeros, Progres dans l'enumeration des posets, C. R. Acad. Sci. Paris 314 serie I (1992) 691-694.

C. Chaunier and N. Lygeros, The Number of Orders with Thirteen Elements, Order 9:3 (1992) 203-204.

C. Chaunier and N. Lygeros, Le nombre de posets a isomorphie pres ayant 12 elements. Theoretical Computer Science, 123 p. 89-94, 1994.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 60.

R. Fraisse and N. Lygeros, Petits posets: denombrement, representabilite par cercles et compenseurs. C. R. Acad. Sci. Paris, 313, I, 417-420, 1991.

D. J. Kleitman and B. L. Rothschild, Asymptotic enumeration of partial orders on a finite set, Trans. Amer. Math. Soc., 205 (1975) 205-220.

N. Lygeros, Calculs exhaustifs sur les posets d'au plus 7 elements. SINGULARITE, vol. 2 n4 p. 10-24, avril 1991.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 1, Chap. 3, pages 96ff; Vol. 2, Problem 5.39, p. 88.

For further references concerning the enumeration of topologies and posets see under A001035.

David Wasserman, Table of n, a(n) for n = 0..16

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 unlabeled topologies and transitive relations.

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

S. R. Finch, Transitive relations, topologies and partial orders

Ann Marie Hess, Mixed Models Site

N. Lygeros and P. Zimmermann, Computation of P(14), the number of posets with 14 elements: 1.338.193.159.771

G. Pfeiffer, Counting Transitive Relations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.2.

Bob Proctor, Chapel Hill Poset Atlas

D. Rusin, Further information and references

N. J. A. Sloane, Classic Sequences

Index entries for sequences related to posets

Index entries for "core" sequences

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 1, Chap. 3, page 98, Fig. 3-1 shows the unlabeled posets with <= 4 points.

Cf. A000798 (labeled topologies), A001035 (labeled posets), A001930 (unlabeled topologies), A006057.

Cf. A079263, A079265.

Sequence in context: A111004 A079566 A059685 this_sequence A127083 A131178 A003149

Adjacent sequences: A000109 A000110 A000111 this_sequence A000113 A000114 A000115

nonn,hard,core,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 04 2006, corrected Jan 15 2006