A394095 - OEIS

%I #14 Jun 10 2026 16:33:37

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

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

%C 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.

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

%H Daniil Naumikhin, <a href="https://github.com/SofaaSogo-oh/2gar-code">Enumeration of binary Convex Structures</a>, GitHub repository.

%H Daniil Naumikhin, <a href="/A394095/a394095.txt">List of convexities for a(3)=61</a>.

%e For n=2 the a(2)=7 binary convexities are following:

%e   {{0, 1}, {}, {0}}

%e   {{0, 1}, {0}}

%e   {{0, 1}, {}, {1}}

%e   {{0, 1}, {}}

%e   {{0, 1}, {1}}

%e   {{0, 1}, {}, {0}, {1}}

%e   {{0, 1}}

%Y Cf. A326878, A000798.

%K nonn,hard,more

%O 0,2

%A _Daniil Naumikhin_, _Aidar Dulliev_, Jun 04 2026