A363512 The number of affine dependencies among the vertices of the n-cube.

1, 20, 1348, 353616, 446148992, 2118502178496, 38636185528212416

Offset: 2

Author

Jörg Rambau, Jun 08 2023

Keywords

• nonn
• hard
• more

Comments

a(n) is also the number of circuits of any point configuration combinatorially equivalent to a unit cube in dimension n.

Examples

			For n = 2, there is only one affine dependence among the vertices of the square involving all points.
For n = 3, since there are 6 embeddings of the square into the boundary and 6 embeddings of the square into the interior of the 3-cube, there are 12 affine dependences on squares; moreover, there is an affine dependence for each of the 8 vertices of the 3-cube coming from the intersection of the line from that vertex to the vertex opposite in the 3-cube with the triangle spanned by the neighbors of that vertex; this adds up to a total of 20 affine dependencies.
		

Links

• Jörg Rambau, Symmetric lexicographic subset reverse search for the enumeration of circuits, cocircuits, and triangulations up to symmetry, Manuscript distributed with TOPCOM.

Crossrefs

Cf. A363506 for the same numbers up to symmetry. Related to A007847 (and A363505, resp.) by oriented-matroid duality.