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%I #20 Jun 08 2023 10:57:42
%S 2,3,6,15,63,623,22432,3899720
%N Number of hyperplanes spanned by the vertices of an n-cube up to symmetry.
%C a(n) is also the number of cocircuits of any point configuration combinatorially equivalent to the unit cube in dimension n up to symmetry.
%H Jörg Rambau, <a href="https://www.wm.uni-bayreuth.de/de/team/rambau_joerg/TOPCOM/SymLexSubsetRS.pdf">Symmetric lexicographic subset reverse search for the enumeration of circuits, cocircuits, and triangulations up to symmetry</a>, Manuscript distributed with <a href="https://www.wm.uni-bayreuth.de/de/team/rambau_joerg/TOPCOM/">TOPCOM</a>.
%e 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.
%e 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.
%Y A007847 gives the total numbers (not up to symmetry). Related to A363506 (and A363512, resp.) by oriented-matroid duality.
%K nonn,hard,more
%O 2,1
%A _Jörg Rambau_, Jun 06 2023
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