[go: up one dir, main page]

login
A363505
Number of hyperplanes spanned by the vertices of an n-cube up to symmetry.
3
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.
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
KEYWORD
nonn,hard,more
AUTHOR
Jörg Rambau, Jun 06 2023
STATUS
approved