I. P. Silva

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20052020

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math.CO2020

Cubes and adjoints of cross-polytopes

J. Lawrence, I. P. Silva

We describe a bijection between oriented cubes and adjoints of cross-polytopes. This correspondence is used to prove that the real affine cube is, up to reorientation in the same c…

math.CO2020

Rectangles, integer vectors and hyperplanes of the hypercube

E. Gioan, I. P. Silva

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 respe…