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

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

Offset

2,1

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.

Links

Table of n, a(n) for n=2..9.

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

Example

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.

Crossrefs

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

Sequence in context: A060796 A059842 A001529 * A069354 A116632 A214343

Adjacent sequences: A363502 A363503 A363504 * A363506 A363507 A363508

Keyword

nonn,hard,more

Author

Jörg Rambau, Jun 06 2023

Status

approved