Rectangles, integer vectors and hyperplanes of the hypercube
Combinatorics
2020-10-01 v1
Abstract
We introduce a family of nonnegative integer vectors - primitive vectors - defining hyperplanes of the real affine cube over and study their properties with respect to the rectangles of the cube. As a consequence we give a short proof that, for small dimensions (), the real affine cube can be recovered from its signed rectangles and its signed cocircuits complementary of its facets and skew-facets.
Cite
@article{arxiv.2009.14275,
title = {Rectangles, integer vectors and hyperplanes of the hypercube},
author = {E. Gioan and I. P. Silva},
journal= {arXiv preprint arXiv:2009.14275},
year = {2020}
}