25 citations · 70 across the 15 of their papers we have counts for
14 papers · 1 filter
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…
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…
Multiplicativity in the theory of coincidence site lattices
Peter Zeiner
Coincidence Site Lattices (CSLs) are a well established tool in the theory of grain boundaries. For several lattices up to dimension , the CSLs are known explicitly as well as…
Well-rounded sublattices and coincidence site lattices
Peter Zeiner
A lattice is called well-rounded, if its lattice vectors of minimal length span the ambient space. We show that there are interesting connections between the existence of well-roun…