A085628 -id:A085628 - cp's OEIS frontend

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

N. J. A. Sloane, Feb 16 2003

Also, number of unconstrained mixed models with n factors.

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.

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.

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

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

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

A091566 Start with 10000 = DIX MILLE in French; to get the next term, replace each single letter with its equivalent Roman number if there is one; read the new number in French and repeat.

Original entry on oeis.org

10000, 500110100015050, 1001100150501100500110050011010001505015001001000115050111000150501001

Offset: 1

Pierre CAMI, Aug 19 2004

The Pfeiffer reference in the links section has nothing to do with this sequence. The A-number, A091566 for this sequence is given in the reference but it is a typo. The reference is relevant to A085628. - Geoffrey Critzer, Jul 28 2014

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

Cf. A096968, A096973.

A355783 Triangular array read by rows. T(n,k) is the number of labeled transitive relations on [n] that have exactly k symmetric points.

Original entry on oeis.org

1, 2, 0, 12, 0, 1, 152, 0, 18, 1, 3504, 0, 456, 24, 10, 135392, 0, 17520, 760, 600, 31, 8321472, 0, 1015440, 35040, 40560, 2316, 361, 784621952, 0, 87375456, 2369360, 3615360, 185556, 52682, 2164, 110521185024, 0, 10984707328, 233001216, 441616000, 19052992, 7723408, 384992, 32663

Offset: 0

Geoffrey Critzer, Jul 16 2022

Let R be a binary relation on [n]. Then x in [n] is a symmetric point of R if there is a y in [n] with x != y and both (x,y),(y,x) in R.

			       1,
       2, 0,
      12, 0,     1,
     152, 0,    18,   1,
    3504, 0,   456,  24,  10,
  135392, 0, 17520, 760, 600, 31

Cf. A280202 (main diagonal), A085628 (column k=0), A006905 (row sums).

nn = 18; A001035 = Cases[Import["https://oeis.org/A001035/b001035.txt",
    "Table"], {, }][[All, 2]]; A[x_] = Sum[A001035[[n + 1]] x^n/n!, {n, 0, nn}];
Table[Take[(Range[0, nn]! CoefficientList[Series[A[Exp[y x] - 1 - y x + x + x], {x, 0, nn}], {x,y}])[[i]], i], {i, 1, nn}] // Grid

E.g.f.: A(exp(y*x) - 1 - y*x + 2*x) where A(x) is the e.g.f. for A001035.

cp's OEIS Frontend

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

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A091566 Start with 10000 = DIX MILLE in French; to get the next term, replace each single letter with its equivalent Roman number if there is one; read the new number in French and repeat.

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A355783 Triangular array read by rows. T(n,k) is the number of labeled transitive relations on [n] that have exactly k symmetric points.

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