Geometriae Dedicata

, Volume 162, Issue 1, pp 271–282

Perfect colourings of cyclotomic integers

  • E. P. Bugarin
  • M. L. A. N. de las Peñas
  • D. Frettlöh
Original Paper

DOI: 10.1007/s10711-012-9726-0

Cite this article as:
Bugarin, E.P., de las Peñas, M.L.A.N. & Frettlöh, D. Geom Dedicata (2013) 162: 271. doi:10.1007/s10711-012-9726-0

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.

Keywords

Colour symmetry Cyclotomic fields Tilings Quasicrystals 

Mathematics Subject Classification

05C25 52C23 11R18 

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • E. P. Bugarin
    • 1
  • M. L. A. N. de las Peñas
    • 2
  • D. Frettlöh
    • 3
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany
  2. 2.Mathematics DepartmentAteneo de Manila UniversityQuezon CityPhilippines
  3. 3.Institut für MathematikBerlinGermany

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