Perfect colourings of cyclotomic integers

Authors

Enrico Paolo Bugarin
Ma. Louise Antonette N. De Las Peñas, Ateneo de Manila UniversityFollow
Dirk Frettlöh, Universitat Bielefeld

Document Type

Article

Publication Date

2013

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.

Recommended Citation

Bugarin, E.P., de las Peñas, M.L.A.N. & Frettlöh, D. Perfect colourings of cyclotomic integers. Geom Dedicata 162, 271–282 (2013). https://doi.org/10.1007/s10711-012-9726-0