E. Paulo Bugarin, M. Louise A.N. de las Penas, Dirk Frettlöh— 2013
Focus Area 1: High-complexity Geometry
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.
Perfect colourings of cyclotomic integers
E. Paulo Bugarin, M. Louise A.N. de las Penas, Dirk Frettlöh