# The coincidence problem for shifted lattices and multilattices

Research paper by Manuel Joseph C. Loquias, Peter Zeiner

Indexed on: 16 Jan '13Published on: 16 Jan '13Published in: Mathematics - Metric Geometry

#### Abstract

A coincidence site lattice is a sublattice formed by the intersection of a lattice \Gamma in $\mathbb{R}^d$ with the image of \Gamma under a linear isometry. Such a linear isometry is referred to as a linear coincidence isometry of \Gamma. Here, we consider the more general case allowing any affine isometry. Consequently, general results on coincidence isometries of shifted copies of lattices, and of multilattices are obtained. In particular, we discuss the shifted square lattice and the diamond packing in detail.