A367565 Number of reduced contexts on n labeled objects.

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.

Links

Table of n, a(n) for n=1..6.

Dmitry I. Ignatov, Introduction to Formal Concept Analysis and Its Applications in Information Retrieval and Related Fields, arXiv:1703.02819 [cs.IR], 2017; RuSSIR 2014, 42-141.

Dmitry I. Ignatov, Supporting iPython code for counting reduced contexts up to n=6 objects, Github repository.

Wikipedia, Formal Concept Analysis.

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

Adjacent sequences: A367562 A367563 A367564 * A367566 A367567 A367568

Keyword

nonn,hard,more

Author

Dmitry I. Ignatov, Nov 23 2023

Status

approved