Coincidence isometries of a shifted square lattice
Metric Geometry
2013-02-21 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.1002.0519,
title = {Coincidence isometries of a shifted square lattice},
author = {Manuel Joseph C. Loquias and Peter Zeiner},
journal= {arXiv preprint arXiv:1002.0519},
year = {2013}
}
Comments
10 pages, 1 figure; paper presented at Aperiodic 2009 (Liverpool)