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arXiv · 1609.03122

Color groups of colorings of $N$-planar modules

Manuel Joseph C. Loquias·Lilibeth D. Valdez·Ma. Lailani B. Walo
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Abstract

A submodule of a $\mathbb{Z}$-module determines a coloring of the module where each coset of the submodule is associated to a unique color. Given a submodule coloring of a $\mathbb{Z}$-module, the group formed by the symmetries of the module that induces a permutation of colors is referred to as the color group of the coloring. In this contribution, a method to solve for the color groups of colorings of $N$-planar modules where $N=4$ and $N=6$ are given. Examples of colorings of rectangular lattices and of the vertices of the Ammann-Beenker tiling are given to exhibit how these methods may be extended to the general case.

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Manuel Joseph C. Loquias, Lilibeth D. Valdez, Ma. Lailani B. Walo. 2016-11-25. Color groups of colorings of $N$-planar modules. https://doi.org/10.1088/1742-6596%2F809%2F1%2F012029

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