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arXiv · 2009.14275

Rectangles, integer vectors and hyperplanes of the hypercube

E. Gioan·I. P. Silva
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Abstract

We introduce a family of nonnegative integer vectors - primitive vectors - defining hyperplanes of the real affine cube over $C^n:=\{-1,1\}^n$ and study their properties with respect to the rectangles of the cube. As a consequence we give a short proof that, for small dimensions ($n\leq 7$), the real affine cube can be recovered from its signed rectangles and its signed cocircuits complementary of its facets and skew-facets.

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E. Gioan, I. P. Silva. 2020-09-29. Rectangles, integer vectors and hyperplanes of the hypercube. https://arxiv.org/abs/2009.14275

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