Acta Crystallographica Section A

Foundations of Crystallography

Volume 65, Part 2 (March 2009)

research papers

 

Sublattice enumeration. IV. Equivalence classes of plane sublattices by parent Patterson symmetry and colour lattice group type

J. S. Rutherford

Abstract: The Dirichlet generating functions for the number of sublattices fixed under each symmetry operation of the parent Patterson group may be combined to count the number of crystallographically nonequivalent sublattices, in total, by sublattice point group and by colour lattice group type. The combinatorial formulae used imply the existence of various congruences among the corresponding arithmetic functions.

Keywords: sublattice enumeration; crystallographically nonequivalent sublattices; colour lattice group; Dirichlet generating functions.

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