A367565 Number of reduced contexts on n labeled objects.

1, 3, 32, 1863, 1316515, 75868099847

Offset: 1

Author

Dmitry I. Ignatov, Nov 23 2023

Keywords

• nonn
• hard
• more

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.

Examples

			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. .
		

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

• 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.

Crossrefs

A047684 (unlabeled version), A102896 (all closure systems).