A235604 - OEIS

%I #16 Oct 15 2022 08:10:00

%S 1,1,1,4,50,7443,95239971

%N Number of equivalence classes of lattices of subsets of the power set 2^[n].

%C This is also the number of inequivalent atomic lattices on n atoms or inequivalent strict closure systems under T1 separation axiom on n elements. - _Dmitry I. Ignatov_, Sep 27 2022

%H Donald M. Davis, <a href="http://arxiv.org/abs/1311.6664">Enumerating lattices of subsets</a>, arXiv preprint arXiv:1311.6664 [math.CO], 2013.

%H Dmitry I. Ignatov, <a href="http://arxiv.org/abs/2209.12256"> On the Cryptomorphism between Davis' Subset Lattices, Atomic Lattices, and Closure Systems under T1 Separation Axiom</a>, arXiv:2209.12256 [cs.DM], 2022.

%Y The number of inequivalent closure operators on a set of n elements where all singletons are closed is given in A355517.

%Y The number of all strict closure operators is given in A102894.

%Y For T_1 closure operators, see A334254.

%K nonn,more,hard

%O 0,4

%A _N. J. A. Sloane_, Jan 21 2014

%E a(5) from _Andrew Weimholt_, Jan 27 2014

%E a(6) from _Dmitry I. Ignatov_, Sep 27 2022