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
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
KEYWORD
nonn,hard,more
AUTHOR
Dmitry I. Ignatov, Nov 23 2023
STATUS
approved