Multiple planar coincidences with N-fold symmetry

Baake, Michael and Grimm, Uwe (2006). Multiple planar coincidences with N-fold symmetry. Zeitschrift für Kristallographie, 221(8) pp. 571–581.

DOI: https://doi.org/10.1524/zkri.2006.221.8.571

Abstract

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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About

• Item ORO ID
• 5815
• Item Type
• Journal Item
• ISSN
• 0044-2968
• Extra Information
• Some of the symbols may not have transferred correctly into this bibliographic record and/or abstract.---
  Preprint version math.MG/0511306 available at http://arxiv.org/abs/math.MG/0511306
• Keywords
• lattices; Coincidence ideals; Planar modules; Cyclotomic fields; Dirichlet series; Asymptotic properties
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Depositing User
• Uwe Grimm