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A000112 Number of partially ordered sets ("posets") with n unlabeled elements.
(Formerly M1495 N0588)
32
1, 1, 2, 5, 16, 63, 318, 2045, 16999, 183231, 2567284, 46749427, 1104891746, 33823827452, 1338193159771, 68275077901156, 4483130665195087 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

REFERENCES

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.

Davison, J. L. Asymptotic enumeration of partial orders. Proceedings of the seventeenth Southeastern international conference on combinatorics, graph theory, and computing (Boca Raton, Fla., 1986). Congr. Numer. 53 (1986), 277--286. MR0885256 (88c:06001)

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. I, 2nd. ed., Chap. 3, pp. 241ff; Vol. 2, Problem 5.39, p. 88.

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

LINKS

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.

G. Brinkmann and B. D. McKay, Posets on up to 16 Points [On Brendan McKay's home page]

G. Brinkmann and B. D. McKay, Posets on up to 16 Points, Order 19 (2) (2002) 147-179.

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

M. Guay-Paquet, A modular relation for the chromatic symmetric functions of (3+1)-free posets, arXiv preprint arXiv:1306.2400, 2013

Ann Marie Hess, Mixed Models Site

DONGSEOK KIM, YOUNG SOO KWON AND JAEUN LEE, Enumerations of finite topologies associated with a finite graph, Arxiv preprint arXiv:1206.0550, 2012. - From N. J. A. Sloane, Nov 09 2012

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

EXAMPLE

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 1, Chap. 3, page 98, Fig. 3-1 (or 2nd. ed., Fig. 3.1, p. 243) shows the unlabeled posets with <= 4 points.

CROSSREFS

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

Cf. A079263, A079265.

Sequence in context: A111004 A079566 A059685 * A205498 A178119 A185998

Adjacent sequences:  A000109 A000110 A000111 * A000113 A000114 A000115

KEYWORD

nonn,hard,more,core,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

a(15)-a(16) are from Brinkmann's and McKay's paper. - Vladeta Jovovic, Jan 04 2006

STATUS

approved

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Last modified April 20 22:29 EDT 2014. Contains 240823 sequences.