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Coincidence isometries of a shifted square lattice

Research paper by Manuel Joseph C. Loquias, Peter Zeiner

Indexed on: 02 Feb '10Published on: 02 Feb '10Published in: Mathematics - Metric Geometry



Abstract

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.