A235604 Number of equivalence classes of lattices of subsets of the power set 2^[n].

1, 1, 1, 4, 50, 7443, 95239971

Offset: 0

Author

N. J. A. Sloane, Jan 21 2014

Keywords

• nonn
• more
• hard

Comments

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

Links

• Donald M. Davis, Enumerating lattices of subsets, arXiv preprint arXiv:1311.6664 [math.CO], 2013.
• Dmitry I. Ignatov, On the Cryptomorphism between Davis' Subset Lattices, Atomic Lattices, and Closure Systems under T1 Separation Axiom, arXiv:2209.12256 [cs.DM], 2022.

Crossrefs

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

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

For T_1 closure operators, see A334254.

Extensions

a(5) from Andrew Weimholt, Jan 27 2014

a(6) from Dmitry I. Ignatov, Sep 27 2022