A000608 - OEIS

A000608

Number of connected partially ordered sets with n unlabeled elements.
(Formerly M2864 N1152)

1, 1, 1, 3, 10, 44, 238, 1650, 14512, 163341, 2360719, 43944974, 1055019099, 32664984238, 1303143553205, 66900392672168, 4413439778321689

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

REFERENCES

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.

E. N. Gilbert, A catalog of partially ordered systems, unpublished memorandum, Aug 08, 1961.

G. Melançon, personal communication.

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).

LINKS

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

Gunnar Brinkmann and Brendan D. McKay, Counting unlabeled topologies and transitive relations.

G. Brinkmann and B. D. McKay, Counting unlabeled topologies and transitive relations, J. Integer Sequences, Volume 8, 2005.

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.

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.

E. N. Gilbert, A catalog of partially ordered systems, unpublished memorandum, Aug 08, 1961. [Annotated scanned copy]

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

N. J. A. Sloane, Transforms

Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 10 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)

N. L. White, Two letters to N. J. A. Sloane, 1970, with hand-drawn enclosure

Wikipedia, Illustration n=4, Illustration n=5, Illustration n=6" (2021)

J. A. Wright, There are 718 6-point topologies, quasiorderings and transgraphs, Preprint, 1970. [Annotated scanned copy]

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, Two related abstracts, 1970 and 1972 [Annotated scanned copies]

J. A. Wright, Letter to N. J. A. Sloane, Apr 06 1972, listing 18 sequences

Index entries for sequences related to posets

MATHEMATICA

A000112 = Cases[Import["https://oeis.org/A000112/b000112.txt", "Table"], {_, _}][[All, 2]];

(* EulerInvTransform is defined in A022562 *)

{1} ~Join~ EulerInvTransform[Rest[A000112]] (* Jean-François Alcover, Dec 04 2019, updated Mar 17 2020 *)

CROSSREFS

Inverse Euler transform of A000112.

Cf. A263864 (multiset transform), A342500 (refined by rank).

Sequence in context: A331156 A240172 A167995 * A333018 A259352 A205803

Adjacent sequences: A000605 A000606 A000607 * A000609 A000610 A000611

KEYWORD

hard,more,nonn,nice

AUTHOR

N. J. A. Sloane, Simon Plouffe, J. A. Wright

EXTENSIONS

More terms from Christian G. Bower, who pointed out connection with A000112, Jan 21 1998 and Dec 12 2001

More terms from Vladeta Jovovic, Jan 04 2006; corrected Jan 15 2006

STATUS

approved