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A363506
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The number of affine dependencies among the vertices of the n-cube up to symmetry.
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3
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OFFSET
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2,2
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COMMENTS
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a(n) is also the number of circuits of any point configuration combinatorially equivalent to a 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, all vertices of the square constitute the only affine dependence.
For n = 3, there is an affine dependence in each boundary square all of which are equivalent; moreover, there is one affine dependence in each square cutting the cube in half all of which are equivalent; the remaining affine dependence with five elements contains a triangle spanned by all neighbors of a point together with that point and the point opposite to it in the 3-cube.
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CROSSREFS
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Cf. A363512 for the total numbers (not up to symmetry). Related to A363505 (and A007847, 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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