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arxiv: math/0608732 · v1 · submitted 2006-08-29 · 🧮 math.GR · math.MG

Indices of Coincidence Isometries of the Hyper Cubic Lattice Z^n

classification 🧮 math.GR math.MG
keywords coincidencecubicformulashyperindexisometrieslatticemathbb
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The problem of computing the index of a coincidence isometry of the hyper cubic lattice $\mathbb{Z}^{n}$ is considered. The normal form of a rational orthogonal matrix is analyzed in detail, and explicit formulas for the index of certain coincidence isometries of $\mathbb{Z}^{n}$ are obtained. These formulas generalize the known results for $n\le 4$.

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