A363505 Number of hyperplanes spanned by the vertices of an n-cube up to symmetry.

2, 3, 6, 15, 63, 623, 22432, 3899720

Offset: 2

Author

Jörg Rambau, Jun 06 2023

Keywords

• nonn
• hard
• more

Comments

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

Examples

			For n = 2, it can be seen that there are only two non-equivalent hyperplanes spanned by vertices of the square: one spanned by a boundary edge having all remaining points on one side and one spanned by a diagonal separating the remaining points.
For n = 3, we again have a hyperplane parallel to a coordinate plane spanned by a boundary square having all the remaining points on one side; moreover, a hyperplane spanned by the four points on the opposite axis-parallel parallel boundary edges of two opposite boundary squares leaving two remaining points on either side, and a skew hyperplane spanned by the three neighbors of a single point separating that point from the remaining points.
		

Links

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

Crossrefs

A007847 gives the total numbers (not up to symmetry). Related to A363506 (and A363512, resp.) by oriented-matroid duality.