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This paper considers the decomposition of a coincidence isometry of a lattice into coincidence reflections and the use of decomposition to study the structure of the coincidence symmetry group.

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This short communication discusses the connections between sublattice counting methods and their relation to Gaussian binomials.

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Explicit formulas for the indices of certain coincidence isometries of the hypercubic lattice are obtained by analyzing the normal form of a rational orthogonal matrix.
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