Color groups of colorings of N-planar modules

13th International Conference on Quasicrystals

Loquias, Manuel Joseph C.^1 ; Valdez, Lilibeth D.^1 ; Walo, Ma. Lailani B.^1

Institute of Mathematics, Natural Sciences Research Institute, University of the Philippines Diliman, Quezon City

1101, Philippines^1

关键词: Rectangular lattices;    Submodules;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/809/1/012029/pdf
DOI  :  10.1088/1742-6596/809/1/012029

来源: IOP

【 摘 要 】

A submodule of a -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 -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.