Baake, Michael and Grimm, Uwe
Multiple planar coincidences with N-fold symmetry.
Zeitschrift für Kristallographie, 221(8) pp. 571–581.
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Planar coincidence site lattices and modules with N-fold symmetry are well understood in a formulation based on cyclotomic fields, in particular for the class number one case, where they appear as certain principal ideals in the corresponding ring of integers. We extend this approach to multiple coincidences, which apply to triple or multiple junctions. In particular, we give explicit results for spectral, combinatorial and asymptotic properties in terms of Dirichlet series generating functions.
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Preprint version math.MG/0511306 available at http://arxiv.org/abs/math.MG/0511306
||lattices; Coincidence ideals; Planar modules; Cyclotomic fields; Dirichlet series; Asymptotic properties
||Mathematics, Computing and Technology > Mathematics and Statistics
||07 Nov 2006
||04 Dec 2010 15:32
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