A394095 Number of 2-ary convexities on a set of n elements.

1, 2, 7, 61, 2271, 600408, 1556743050

Offset

0,2

Comments

A convexity G on as 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.

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.

Daniil Naumikhin, List of convexities for a(3)=61.

Example

For n=2 the a(2)=7 binary convexities are following:
  {{0, 1}, {}, {0}}
  {{0, 1}, {0}}
  {{0, 1}, {}, {1}}
  {{0, 1}, {}}
  {{0, 1}, {1}}
  {{0, 1}, {}, {0}, {1}}
  {{0, 1}}

Crossrefs

Cf. A326878, A000798.

Sequence in context: A363655 A089307 A367902 * A395589 A102896 A088107

Adjacent sequences: A394092 A394093 A394094 * A394096 A394097 A394098

Keyword

nonn,hard,more

Author

Daniil Naumikhin, Aidar Dulliev, Jun 04 2026

Status

approved