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A193674 Number of nonisomorphic systems enumerated by A102896; that is, the number of inequivalent closure operators (or Moore families). 19
1, 2, 5, 19, 184, 14664, 108295846, 2796163199765896 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also the number of unlabeled n-vertex set-systems (A003180) closed under union. - Gus Wiseman, Aug 01 2019

REFERENCES

D. E. Knuth, The Art of Computer Programming, Vol. 4, Section 7.1.1

LINKS

Table of n, a(n) for n=0..7.

Daniel Borchmann, Bernhard Ganter, Concept Lattice Orbifolds - First Steps, Proceedings of the 7th International Conference on Formal Concept Analysis (ICFCA 2009), 22-37 (Reference points to A108799).

G. Brinkmann and R. Deklerck, Generation of Union-Closed Sets and Moore Families, arXiv:1701.03751 [math.CO], 2017.

G. Brinkmann and R. Deklerck, Generation of Union-Closed Sets and Moore Families, Journal of Integer Sequences, Vol.21 (2018), Article 18.1.7.

P. Colomb, A. Irlande and O. Raynaud, Counting of Moore Families for n=7, International Conference on Formal Concept Analysis (2010).

FORMULA

a(n) = A193675(n)/2.

EXAMPLE

From Gus Wiseman, Aug 01 2019: (Start)

Non-isomorphic representatives of the a(0) = 1 through a(3) = 19 set-systems closed under union:

{} {} {} {}

{{1}} {{1}} {{1}}

{{1,2}} {{1,2}}

{{2},{1,2}} {{1,2,3}}

{{1},{2},{1,2}} {{2},{1,2}}

{{3},{1,2,3}}

{{1},{2},{1,2}}

{{2,3},{1,2,3}}

{{1},{2,3},{1,2,3}}

{{3},{2,3},{1,2,3}}

{{1,3},{2,3},{1,2,3}}

{{2},{3},{2,3},{1,2,3}}

{{2},{1,3},{2,3},{1,2,3}}

{{3},{1,3},{2,3},{1,2,3}}

{{1,2},{1,3},{2,3},{1,2,3}}

{{2},{3},{1,3},{2,3},{1,2,3}}

{{3},{1,2},{1,3},{2,3},{1,2,3}}

{{2},{3},{1,2},{1,3},{2,3},{1,2,3}}

{{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}

(End)

CROSSREFS

Cf. A102894, A102895, A102897.

The labeled case is A102896.

The covering case is A108798.

The same for intersection instead of union is A108800.

The case with empty edges allowed is A193675.

Cf. A000612, A001930, A003180, A306445, A326875, A326883.

Sequence in context: A304981 A284860 A108799 * A085871 A202422 A212269

Adjacent sequences: A193671 A193672 A193673 * A193675 A193676 A193677

KEYWORD

nonn,hard,more

AUTHOR

Don Knuth, Jul 01 2005

EXTENSIONS

a(6) received Aug 17 2005

a(6) corrected by Pierre Colomb, Aug 02 2011

a(7) from Gunnar Brinkmann, Feb 07 2018

STATUS

approved

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Last modified December 7 05:41 EST 2022. Contains 358649 sequences. (Running on oeis4.)