A000112 -id:A000112 - cp's OEIS frontend

A124480 Number of hook length posets with n elements.

Original entry on oeis.org

1, 2, 4, 10, 23, 63, 165

Offset: 1

Franklin T. Adams-Watters, Nov 03 2006

Cheryl A. Gann and Robert A. Proctor, Poset Counts
Robert A. Proctor, Definition of hook length poset

Cf. A000112, A124481, A124482, A124483, A124016.

A124481 Number of connected hook length posets, with n elements.

Original entry on oeis.org

1, 1, 2, 5, 11, 31, 75, 232, 607

Offset: 1

Franklin T. Adams-Watters, Nov 03 2006

Cheryl A. Gann and Robert A. Proctor, Poset Counts
Robert A. Proctor, Definition of hook length poset

Cf. A000112, A124480, A124482, A124483.

A331156 Number of (weakly) connected gluing-parallel or GP-posets with n points.

Original entry on oeis.org

1, 1, 1, 3, 10, 44, 233

Offset: 0

N. J. A. Sloane, Jan 16 2020, following a suggestion from Michael De Vlieger

Uli Fahrenberg, Christian Johansen, Georg Struth, Ratan Bahadur Thapa, Generating Posets Beyond N, arXiv:1910.06162 [cs.FL], 2019.

The seven sequences in the table of Uli Fahrenberg et al., 2019, are A000112, A003430, A079566, A331156, A331157, A331158, A331159.

Typo in a(6) corrected by Uli Fahrenberg, Feb 03 2024

A331157 Number of iposets (posets with interfaces) with starting interfaces only, with n points.

Original entry on oeis.org

1, 2, 5, 16, 66, 350

Offset: 0

N. J. A. Sloane, Jan 16 2020, following a suggestion from Michael De Vlieger

Uli Fahrenberg, Christian Johansen, Georg Struth, Ratan Bahadur Thapa, Generating Posets Beyond N, arXiv:1910.06162 [cs.FL], 2019.

The seven sequences in the table of Uli Fahrenberg et al., 2019, are A000112, A003430, A079566, A331156, A331157, A331158, A331159.

A331158 Number of iposets (posets with interfaces) with n points.

Original entry on oeis.org

1, 4, 17, 86, 532, 4068, 38933, 474822, 7558620

Offset: 0

N. J. A. Sloane, Jan 16 2020, following a suggestion from Michael De Vlieger

Uli Fahrenberg, Christian Johansen, Georg Struth, Ratan Bahadur Thapa, Generating Posets Beyond N, arXiv:1910.06162 [cs.FL], 2019.
Uli Fahrenberg, Christian Johansen, Georg Struth, Krzysztof Ziemiański, Posets with Interfaces for Concurrent Kleene Algebra, arxiv:2106.10895 [cs.FL], 2021.

The seven sequences in the table of Uli Fahrenberg et al., 2019, are A000112, A003430, A079566, A331156, A331157, A331158, A331159.

a(5)-a(8) from Uli Fahrenberg, Jun 22 2021

A331159 Number of GP-iposets (gluing-parallel posets with interfaces) with n points.

Original entry on oeis.org

1, 4, 16, 74, 419, 2980, 26566, 289279, 3726311

Offset: 0

N. J. A. Sloane, Jan 16 2020, following a suggestion from Michael De Vlieger

Uli Fahrenberg, Christian Johansen, Georg Struth, Ratan Bahadur Thapa, Generating Posets Beyond N, arXiv:1910.06162 [cs.FL], 2019.
Uli Fahrenberg, Christian Johansen, Georg Struth, Krzysztof Ziemiański, Posets with Interfaces for Concurrent Kleene Algebra, arxiv:2106.10895 [cs.FL], 2021.

The seven sequences in the table of Uli Fahrenberg et al., 2019, are A000112, A003430, A079566, A331156, A331157, A331158, A331159.

a(7)-a(8) from Uli Fahrenberg, Jun 22 2021

A001928 Number of connected topologies with n unlabeled nodes.

Original entry on oeis.org

1, 1, 2, 6, 21, 94, 512, 3485, 29515, 314474, 4255727, 73831813, 1653083021, 47941962135, 1803010446411, 87882300251730, 5543501326580737

Offset: 0

N. J. A. Sloane

K. K.-H. Butler and G. Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184.
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).
J. A. Wright, There are 718 6-point topologies, quasi-orderings and transgraphs, Notices Amer. Math. Soc., 17 (1970), p. 646, Abstract #70T-A106.
J. A. Wright, personal communication.

K. K.-H. Butler and G. Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184
K. K.-H. Butler and G. Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184. [Annotated scan of pages 180 and 183 only]
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
Henry Sharp, Jr., Quasi-orderings and topologies on finite sets, Proceedings of the American Mathematical Society 17.6 (1966): 1344-1349. [Annotated scanned copy]
N. J. A. Sloane, List of sequences related to partial orders, circa 1972
J. A. Wright, There are 718 6-point topologies, quasiorderings and transgraphs, Preprint, 1970 [Annotated scanned copy]
J. A. Wright, Letter to N. J. A. Sloane, Apr 06 1972, listing 18 sequences

Cf. A001929, A001930.

A001930 = Cases[Import["https://oeis.org/A001930/b001930.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
{1} ~Join~ EulerInvTransform[Rest[A001930]] (* Jean-François Alcover, Jan 01 2020, updated Mar 17 2020 *)

Inverse Euler transform of A001930. - Vladeta Jovovic, Jan 06 2006

More terms from Vladeta Jovovic, Jan 06 2006

A079263 Number of constrained mixed models with n factors.

Original entry on oeis.org

2, 6, 22, 101, 576, 4162, 38280, 451411, 6847662, 133841440

Offset: 1

N. J. A. Sloane, Feb 16 2003

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.
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

Cf. A000112, A079265, A006126, A006602, A006896-A006898.

a(10) from Bayon, Lygeros, and Sereni (2005) added by Sean A. Irvine, Aug 05 2025

A124483 Number of connected jeu de taquin posets with n elements.

Original entry on oeis.org

1, 1, 2, 5, 11, 32, 77, 236, 616

Offset: 1

Franklin T. Adams-Watters, Nov 03 2006

Cheryl A. Gann and Robert A. Proctor, Poset Counts
Robert A. Proctor, Definition of the JDT Property

Cf. A000112, A124480, A124481, A124483.

A133983 Number of nonisomorphic n-element self-dual posets (or partially ordered sets).

Original entry on oeis.org

1, 2, 3, 8, 15, 50, 119, 493, 1521, 7924, 30783, 209818

Offset: 1

Richard Stanley, Jan 08 2008

Posets whose Hasse diagram looks the same if it is turned upside down. - N. J. A. Sloane, Mar 22 2013

R. P. Stanley, Enumerative Combinatorics I, 2nd. ed., p. 247.

Cf. A000112.

for n in range(1,10): print(len([P for P in Posets(n) if P.is_selfdual()])) # Jori Mäntysalo, Oct 02 2014

a(9) from Jori Mäntysalo, Oct 02 2014

a(10-12) from Rico Zöllner and Konrad Handrich, Oct 22 2024

cp's OEIS Frontend

A124480 Number of hook length posets with n elements.

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A124481 Number of connected hook length posets, with n elements.

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A331156 Number of (weakly) connected gluing-parallel or GP-posets with n points.

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A331157 Number of iposets (posets with interfaces) with starting interfaces only, with n points.

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A331158 Number of iposets (posets with interfaces) with n points.

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A331159 Number of GP-iposets (gluing-parallel posets with interfaces) with n points.

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A001928 Number of connected topologies with n unlabeled nodes.

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Mathematica

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A079263 Number of constrained mixed models with n factors.

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A124483 Number of connected jeu de taquin posets with n elements.

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Keywords

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A133983 Number of nonisomorphic n-element self-dual posets (or partially ordered sets).

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Sage

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