Bravais colourings of planar modules with N-fold symmetry
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Michael Baake
Abstract
The first step in investigating colour symmetries for periodic and aperiodic systems is the determination of all colouring schemes that are compatible with the symmetry group of the underlying structure, or with a subgroup of it. For an important class of colourings of planar structures, this mainly combinatorial question can be addressed with methods of algebraic number theory. We present the corresponding results for all planar modules with N-fold symmetry that emerge as the rings of integers in cyclotomic fields with class number one. The counting functions are multiplicative and can be encapsulated in Dirichlet series generating functions, which turn out to be the Dedekind zeta functions of the corresponding cyclotomic fields.
© 2004 Oldenbourg Wissenschaftsverlag GmbH
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- Twin point groups and the polychromatic symmetry of twins
- Bravais colourings of planar modules with N-fold symmetry
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Articles in the same Issue
- Twin point groups and the polychromatic symmetry of twins
- Bravais colourings of planar modules with N-fold symmetry
- Intensity distribution of the eight-beam case of the Si-888 reflection in backscattering geometry
- Crystal structures of GaX3 (X = Cl, Br, I) and AlI3
- Two new ammonium diphosphates: crystal structure of Mn0.5NH4H2P2O7·H2O and MnNaNH4P2O7·3H2O
- ´Pseudopolymorphs′ of 3aβ,4α-dihydro-4β,10-dimethyl-2-phenyl-1H,3H,5H-pyrrolo[3,4-b]carbazol-1,3-dione
- On racemic and L-malates: a comparison of their crystal structures
- Crystal and electronic structure of aqua(N-salicylidene-methylester-l-glutamato)Cu(II) monohydrate
