A394616 Number of strict non-grounded 2-ary convexities on a set of n elements.

0, 1, 3, 16, 209, 10806, 3569509

Offset

0,3

Comments

A convexity G on a set X is n-ary if its convex sets are precisely the sets A with the property that co(B) is a subset of A for each subset B with cardinality no more than n. A strict non-grounded convexity is one that does not contain an empty set.

References

M. L. J. van de Vel, Theory of Convex Structures, North-Holland Mathematical Library, vol. 50, North-Holland, Amsterdam, 1993.

Links

Table of n, a(n) for n=0..6.

Daniil Naumikhin, Enumeration of binary Convex Structures, GitHub repository.

Example

For n=2 the a(2)=3 strict non-grounded binary convexities are following:
  {{0, 1}, {0}},
  {{0, 1}, {1}},
  {{0, 1}}.

Crossrefs

Cf. A326878, A000798, A394095.

Sequence in context: A196562 A317073 A272658 * A326903 A113597 A361366

Adjacent sequences: A394612 A394613 A394614 * A394617 A394618 A394619

Keyword

nonn,hard,more,new

Author

Daniil Naumikhin and Aidar Dulliev, Jun 18 2026

Status

approved