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Perfect colourings of cyclotomic integers |
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| Authors: | E. P. Bugarin M. L. A. N. de las Peñas D. Frettlöh |
| Affiliation: | 1. Fakult?t für Mathematik, Universit?t Bielefeld, 33501, Bielefeld, Germany 2. Mathematics Department, Ateneo de Manila University, Loyola Heights, 1108, Quezon City, Philippines 3. Institut für Mathematik, FU Berlin, 14195, Berlin, Germany |
| Abstract: | Perfect colourings of the rings of cyclotomic integers of class number one are studied. It is shown that all colourings induced by ideals (q) are chirally perfect, and vice versa. A necessary and sufficient condition for a colouring to be perfect is obtained, depending on the factorisation of q. This result yields the colour symmetry group H in general. Furthermore, the colour preserving group K is determined in all but finitely many cases. An application to colourings of quasicrystals is given. |
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