Bravais colourings of planar modules with N-fold symmetry

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dc.creatorBaake, Michael
dc.creatorGrimm, Uwe
dc.date2003-01-03
dc.date2006-06-26
dc.date.accessioned2026-07-07T06:35:33Z
dc.date.available2026-07-07T06:35:33Z
dc.descriptionThe 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.
dc.description8 pages, references updated, see also math.MG/0511147 and math.MG/0511306 for related work on single and multiple coincidences
dc.identifierhttps://arxiv.org/abs/math/0301021
dc.identifierhttp://arxiv.org/abs/math/0301021
dc.identifierZeitschrift f. Kristallographie 219 (2004) 72-80
dc.identifierdoi:10.1524/zkri.219.2.72.26322
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99828
dc.subjectCombinatorics
dc.subjectMathematical Physics
dc.subjectMetric Geometry
dc.subject05A15, 52C20, 52C23, 11R99
dc.titleBravais colourings of planar modules with N-fold symmetry
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