Search: id:A000112
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%I A000112 M1495 N0588
%S A000112 1,1,2,5,16,63,318,2045,16999,183231,2567284,46749427,1104891746,
%T A000112 33823827452,1338193159771,68275077901156,4483130665195087
%N A000112 Number of partially ordered sets ("posets") with n unlabeled elements.
%C A000112 Also fixed effects ANOVA models with n factors, which may be both crossed 
               and nested.
%C A000112 [ a(15)-a(16) are from Brinkmann's and McKay's paper ] - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), Jan 04 2006
%D A000112 G. Birkhoff, Lattice Theory, 1961, p. 4.
%D A000112 C. Chaunier and N. Lygeros, Progres dans l'enumeration des posets, C. 
               R. Acad. Sci. Paris 314 serie I (1992) 691-694.
%D A000112 C. Chaunier and N. Lygeros, The Number of Orders with Thirteen Elements, 
               Order 9:3 (1992) 203-204.
%D A000112 C. Chaunier and N. Lygeros, Le nombre de posets a isomorphie pres ayant 
               12 elements. Theoretical Computer Science, 123 p. 89-94, 1994.
%D A000112 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 60.
%D A000112 R. Fraisse and N. Lygeros, Petits posets: denombrement, representabilite 
               par cercles et compenseurs. C. R. Acad. Sci. Paris, 313, I, 417-420, 
               1991.
%D A000112 D. J. Kleitman and B. L. Rothschild, Asymptotic enumeration of partial 
               orders on a finite set, Trans. Amer. Math. Soc., 205 (1975) 205-220.
%D A000112 N. Lygeros, Calculs exhaustifs sur les posets d'au plus 7 elements. SINGULARITE, 
               vol. 2 n4 p. 10-24, avril 1991.
%D A000112 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000112 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000112 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 1, Chap. 3, 
               pages 96ff; Vol. 2, Problem 5.39, p. 88.
%D A000112 For further references concerning the enumeration of topologies and posets 
               see under A001035.
%H A000112 David Wasserman, <a href="b000112.txt">Table of n, a(n) for n = 0..16</
               a>
%H A000112 R. Bayon, N. Lygeros and J.-S. Sereni, <a href="http://www.math.nthu.edu.tw/
               ~amen/2005/040909-2.pdf">New progress in enumeration of mixed models</
               a>, Applied Mathematics E-Notes, 5 (2005), 60-65.
%H A000112 R. Bayon, N. Lygeros and J.-S. Sereni, <a href="http://www-sop.inria.fr/
               mascotte/personnel/Jean-Sebastien.Sereni/Articles/BLS03.pdf">Nouveaux 
               progr\`es dans l'\'enum\'eration des mod\`eles mixtes</a>, in Knowledge 
               discovery and discrete mathematics : JIM'2003, INRIA, Universit\'e 
               de Metz, France, 2003, pp. 243-246.
%H A000112 Gunnar Brinkmann and Brendan D. McKay, <a href="http://cs.anu.edu.au/
               ~bdm/papers/topologies.pdf">Counting unlabeled topologies and transitive 
               relations</a>.
%H A000112 P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               Sequences realized by oligomorphic permutation groups</a>, J. Integ. 
               Seqs. Vol. 3 (2000), #00.1.5.
%H A000112 S. R. Finch, <a href="http://algo.inria.fr/bsolve/">Transitive relations, 
               topologies and partial orders</a>
%H A000112 Ann Marie Hess, <a href="http://www.stat.colostate.edu/~hess/MixedModels.htm">
               Mixed Models Site</a>
%H A000112 N. Lygeros and P. Zimmermann, <a href="http://www.lygeros.org/Math/poset.html">
               Computation of P(14), the number of posets with 14 elements: 1.338.193.159.771</
               a>
%H A000112 G. Pfeiffer, <a href="http://www.cs.uwaterloo.ca/journals/JIS/">Counting 
               Transitive Relations</a>, Journal of Integer Sequences, Vol. 7 (2004), 
               Article 04.3.2.
%H A000112 Bob Proctor, <a href="http://www.unc.edu/~rap/Posets/">Chapel Hill Poset 
               Atlas</a>
%H A000112 D. Rusin, <a href="http://www.math.niu.edu/~rusin/known-math/97/finite.top">
               Further information and references</a>
%H A000112 N. J. A. Sloane, <a href="classic.html#POSETS">Classic Sequences</a>
%H A000112 <a href="Sindx_Pos.html#posets">Index entries for sequences related to 
               posets</a>
%H A000112 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%e A000112 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 1, Chap. 3, 
               page 98, Fig. 3-1 shows the unlabeled posets with <= 4 points.
%Y A000112 Cf. A000798 (labeled topologies), A001035 (labeled posets), A001930 (unlabeled 
               topologies), A006057.
%Y A000112 Cf. A079263, A079265.
%Y A000112 Sequence in context: A111004 A079566 A059685 this_sequence A127083 A131178 
               A003149
%Y A000112 Adjacent sequences: A000109 A000110 A000111 this_sequence A000113 A000114 
               A000115
%K A000112 nonn,hard,core,nice
%O A000112 0,3
%A A000112 N. J. A. Sloane (njas(AT)research.att.com).
%E A000112 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 04 2006, corrected 
               Jan 15 2006

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