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A367565
Number of reduced contexts on n labeled objects.
0
1, 3, 32, 1863, 1316515, 75868099847
OFFSET
1,2
COMMENTS
Equivalently, number of set systems on n points such that each of the systems obtained from the corresponding closure system on n points by omitting all intersections of other sets in the system and the set {1,...,n}; the systems with all sets shared at least one common element are not allowed.
This is the labeled version of A047684.
REFERENCES
B. Ganter and R. Wille, Formal Concept Analysis, Springer-Verlag, 1999, ISBN 3-540-62771-5, p. 24.
B. Ganter and S. A. Obiedkov, Conceptual Exploration, Springer 2016, ISBN 978-3-662-49290-1, pages 1-315.
EXAMPLE
The a(2)=3 set systems are {{1},{2}}, {{},{1}}, and {{},{2}}. The corresponding formal contexts represented by crosstables are
1 x. 1 .x 1 ..
2 .x 2 .. 2 x. .
CROSSREFS
A047684 (unlabeled version), A102896 (all closure systems).
Sequence in context: A368601 A054780 A203323 * A222683 A134474 A096469
KEYWORD
nonn,hard,more
AUTHOR
Dmitry I. Ignatov, Nov 23 2023
STATUS
approved