Perfect colourings of cyclotomic integers

  title={Perfect colourings of cyclotomic integers},
  author={E. Bugarin and M. L. A. N. Penas and D. Frettl{\"o}h},
  journal={Geometriae Dedicata},
  • E. Bugarin, M. L. A. N. Penas, D. Frettlöh
  • Published 2009
  • Mathematics
  • Geometriae Dedicata
  • 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… CONTINUE READING
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