Coincidence isometries of a shifted square lattice

Details Coincidence isometries of a shifted square lattice Coincidence isometries of a shifted square lattice

2010-02-02

arxiv.org/abs/1002.0519v1

Mathematics

Metric Geometry

10 pages, 1 figure; paper presented at Aperiodic 2009 (Liverpool)

Scientific paper

10.1088/1742-6596/226/1/012026

We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the coincidence site lattices of a shifted square lattice by identifying the square lattice with the ring of Gaussian integers. To illustrate them, we calculate the set of coincidence isometries, as well as generating functions for the number of coincidence site lattices and coincidence isometries, for specific examples.

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