Perfect colourings of cyclotomic integers

• Main Authors: Bugarin, Enrico Paolo, De Las Peñas, Ma. Louise Antonette N, Frettlöh, Dirk
• Format: text
• Published: Archīum Ateneo 2013
• Subjects: Colour symmetry; Cyclotomic fields; Tilings; Quasicrystals; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/27; https://arxiv.org/abs/0905.4048
• Institution: Ateneo De Manila University

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. Thi...