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arXiv · 1506.00028

Coincidence indices of sublattices and coincidences of colorings

Manuel Joseph C. Loquias·Peter Zeiner
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Abstract

Even though a lattice and its sublattices have the same group of coincidence isometries, the coincidence index of a coincidence isometry with respect to a lattice $\Lambda_1$ and to a sublattice $\Lambda_2$ may differ. Here, we examine the coloring of $\Lambda_1$ induced by $\Lambda_2$ to identify how the coincidence indices with respect to $\Lambda_1$ and to $\Lambda_2$ are related. This leads to a generalization of the notion of color symmetries of lattices to what we call color coincidences of lattices. Examples involving the cubic and hypercubic lattices are given to illustrate these ideas.

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Manuel Joseph C. Loquias, Peter Zeiner. 2015-05-29. Coincidence indices of sublattices and coincidences of colorings. https://doi.org/10.1515/zkri-2015-1864

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