Cubes of integral vectors in dimension four

Details Cubes of integral vectors in dimension four Cubes of integral vectors in dimension four

2011-08-15

arxiv.org/abs/1108.3113v1

Mathematics

Number Theory

11 pages

Scientific paper

A system of $m$ nonzero vectors in $\mathbb{Z}^n$ is called an $m$-icube if
they are pairwise orthogonal and have the same length. The paper describes
$m$-icubes in $\mathbb{Z}^4$ for $2\le m\le 4$ using Hurwitz integral
quaternions, counts the number of them with given edge length, and proves that
unlimited extension is possible in $\mathbb{Z}^4$.

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