A006966 Number of lattices on n unlabeled nodes.

1, 1, 1, 1, 2, 5, 15, 53, 222, 1078, 5994, 37622, 262776, 2018305, 16873364, 152233518, 1471613387, 15150569446, 165269824761, 1901910625578, 23003059864006

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more
• nice
• core

Comments

Also commutative idempotent monoids. Also commutative idempotent semigroups of order n-1.

Commutative idempotent semigroups are also called semilattices, so A(n) counts semilattices of order n-1. - Dennis Sweeney, Jul 19 2024

References

• J. Heitzig and J. Reinhold, Counting finite lattices, Algebra Universalis, 48 (2002), 43-53.
• P. D. Lincoln, personal communication.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• J. R. Stembridge, personal communication.

Links

• David Wasserman and Nathan Lawless, Table of n, a(n) for n = 0..20 (a(20) from _Volker Gebhardt_)
• R. Belohlavek and V. Vychodil, Residuated lattices of size <=12, Order 27 (2010) 147-161 doi:10.1007/s11083-010-9143-7, Table 2.
• V. Gebhardt and S. Tawn, Constructing unlabelled lattices, arXiv:1609.08255 [math.CO], 2016.
• D. J. Greenhoe, MRA-Wavelet subspace architecture for logic, probability, and symbolic sequence processing, 2014.
• J. Heitzig and J. Reinhold, Counting finite lattices, preprint no. 298, Institut für Mathematik, Universität Hannover, Germany, 1999.
• J. Heitzig and J. Reinhold, Counting finite lattices, CiteSeer 1999.
• P. Jipsen and N. Lawless, Generating all modular lattices of a given size (preprint)
• D. J. Kleitman and K. J. Winston, The asymptotic number of lattices, in: Combinatorial mathematics, optimal designs and their applications (Proc. Sympos. Combin. Math. and Optimal Design, Colorado State Univ., Fort Collins, Colo., 1978), Ann. Discrete Math. 6 (1980), 243-249.
• S. Kyuno, An inductive algorithm to construct finite lattices, Math. Comp. 33 (1979), no. 145, 409-421.
• N. Lawless, Generating all modular lattices of a given size, Slides, ADAM 2013.
• Arman Shamsgovara, Enumerating, Cataloguing and Classifying All Quantales on up to Nine Elements, In: Glück, R., Santocanale, L., and Winter, M. (eds), Relational and Algebraic Methods in Computer Science (RAMiCS 2023) Lecture Notes in Computer Science, Springer, Cham, Vol. 13896.
• Wikipedia, Semilattice.
• Richard Stanley, MathOverflow: Semilattices with n elements
• Index entries for sequences related to semigroups
• Index entries for "core" sequences

Crossrefs

Cf. A006981, A006982, A055512. Main diagonal of A058142. a(n+1) is main diagonal of A058116.

Extensions

More terms from Jobst Heitzig (heitzig(AT)math.uni-hannover.de), Jul 03 2000

a(19) from Nathan Lawless, Sep 15 2013

a(20) from Volker Gebhardt, Sep 28 2016