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A363505
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Number of hyperplanes spanned by the vertices of an n-cube up to symmetry.
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3
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OFFSET
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2,1
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COMMENTS
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a(n) is also the number of cocircuits of any point configuration combinatorially equivalent to the unit cube in dimension n up to symmetry.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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A007847 gives the total numbers (not up to symmetry). Related to A363506 (and A363512, resp.) by oriented-matroid duality.
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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