25 citations · 70 across the 15 of their papers we have counts for
16 papers
Geometric enumeration problems for lattices and embedded -modules
Michael Baake, Peter Zeiner
In this review, we count and classify certain sublattices of a given lattice, as motivated by crystallography. We use methods from algebra and algebraic number theory to find and e…
Coincidence indices of sublattices and coincidences of colorings
Manuel Joseph C. Loquias, Peter Zeiner
Even though a lattice and its sublattices have the same group of coincidence isometries, the coincidence index of a coincidence isometry with respect to a lattice and to a su…
Similar submodules and coincidence site modules
Peter Zeiner
We consider connections between similar sublattices and coincidence site lattices (CSLs), and more generally between similar submodules and coincidence site modules of general (fre…
Well-rounded sublattices of planar lattices
Michael Baake, Rudolf Scharlau, Peter Zeiner
A lattice in Euclidean -space is called well-rounded if it contains linearly independent vectors of minimal length. This class of lattices is important for various questions…
CSLs of the root lattice
Manuela Heuer, Peter Zeiner
Recently, the group of coincidence isometries of the root lattice has been determined providing a classification of these isometries with respect to their coincidence indices…
The coincidence problem for shifted lattices and crystallographic point packings
Manuel Joseph C. Loquias, Peter Zeiner
A coincidence site lattice is a sublattice formed by the intersection of a lattice in with the image of under a linear isometry. Such a linear isometry is re…