A367565 - OEIS

%I #14 Nov 27 2023 10:29:40

%S 1,3,32,1863,1316515,75868099847

%N Number of reduced contexts on n labeled objects.

%C 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.

%C This is the labeled version of A047684.

%D B. Ganter and R. Wille, Formal Concept Analysis, Springer-Verlag, 1999, ISBN 3-540-62771-5, p. 24.

%D B. Ganter and S. A. Obiedkov, Conceptual Exploration, Springer 2016, ISBN 978-3-662-49290-1, pages 1-315.

%H Dmitry I. Ignatov, <a href="http://arxiv.org/abs/1703.02819">Introduction to Formal Concept Analysis and Its Applications in Information Retrieval and Related Fields</a>, arXiv:1703.02819 [cs.IR], 2017; RuSSIR 2014, 42-141.

%H Dmitry I. Ignatov, <a href="https://github.com/dimachine/ReducedContexts/">Supporting iPython code for counting reduced contexts up to n=6 objects</a>, Github repository.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Formal_concept_analysis">Formal Concept Analysis</a>.

%e The a(2)=3 set systems are {{1},{2}}, {{},{1}}, and {{},{2}}. The corresponding formal contexts represented by crosstables are

%e     1 x.    1 .x    1 ..

%e     2 .x    2 ..    2 x. .

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

%K nonn,hard,more

%O 1,2

%A _Dmitry I. Ignatov_, Nov 23 2023