Multiple planar coincidences with N-fold symmetry

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.

13 pages, two figures. For previous related work see math.MG/0511147 and math.CO/0301021. Minor changes and references updated

References in corpus (3)

• Planar coincidences for N-fold symmetry
• Bravais colourings of planar modules with N-fold symmetry
• A Note on Shelling

Cited by in corpus (6)

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• Multiplicativity in the theory of coincidence site lattices
• Coincidences of a shifted hexagonal lattice and the hexagonal packing