A363506 The number of affine dependencies among the vertices of the n-cube up to symmetry.

1, 3, 15, 186, 12628, 3591868, 3858105362

Offset: 2

Author

Jörg Rambau, Jun 06 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 up to symmetry.

Examples

			For n = 2, all vertices of the square constitute the only affine dependence.
For n = 3, there is an affine dependence in each boundary square all of which are equivalent; moreover, there is one affine dependence in each square cutting the cube in half all of which are equivalent; the remaining affine dependence with five elements contains a triangle spanned by all neighbors of a point together with that point and the point opposite to it in the 3-cube.
		

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. A363512 for the total numbers (not up to symmetry). Related to A363505 (and A007847, resp.) by oriented-matroid duality.