A386593 Number of sub-relation-algebras of Re(n), the collection of all binary relations over {1,2,...,n}.

1, 2, 6, 30, 124

Offset: 1

Author

Jeremy F. Alm, Jul 26 2025

Keywords

• nonn
• hard
• more

Comments

The first four terms are not that difficult to verify. In fact, for n < 5 the subalgebra lattice of Re(n) is the dual of the subgroup lattice of S_n. Hence a(n) = A005432(n) for n < 5.

Relation algebras are closed under union, intersection, complement, composition, inverse, and identity.

References

• Bjarni Jónsson, Maximal algebras of binary relations. In: Contributions to Group Theory, Contemporary Mathematics, vol. 33, pp. 299-307. Amer. Math. Soc., Providence (1984).

Crossrefs

Cf. A005432.