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There is a six-dimensional counterexample: $(+1,+1,+1,+1,+1,+1)$ $(-1,-1,+1,+1,+1,+1)$ $(+1,+1,-1,-1,+1,+1)$ $(+1,+1,+1,-1,-1,+1)$ $(+1,-1,+1,-1,+1,-1)$ The normal to the linear span of these five …

Recall that the face-centred cubic lattice comprises all vectors in $\mathbb{Z}^3$ whose coordinate sum is even. Let $(x, y, z) \in \mathbb{R}^3$. For each coordinate, define the discrepancy to be th …

Let $X$ be an $n \times n$ invertible square matrix over some field $\mathbb{F}$, and let $Y = XX^T$ be the product of the matrix with its transpose. When $\mathbb{F} = \mathbb{R}$, $Y$ is positive-d …

There are polynomial-time reductions from your problem to Graph Isomorphism and vice-versa. As a quick definition, when I speak of 'subdividing' an edge, I mean to replace each edge $u, v$ with a pat …

The following comment in the question intrigued me: In fact, it's possible to show that the linear symmetries of $\mathbb{R}^6$ that preserve the Cayley-Menger determinant form the Weyl group $D_6$, …