Well-rounded sublattices and coincidence site lattices

Peter Zeiner

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arXiv · 1210.0571

Well-rounded sublattices and coincidence site lattices

Peter Zeiner

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Abstract

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-rounded sublattices and coincidence site lattices (CSLs). Furthermore, we count the number of well-rounded sublattices for several planar lattices and give their asymptotic behaviour.

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Peter Zeiner. 2012-10-01. Well-rounded sublattices and coincidence site lattices. https://arxiv.org/abs/1210.0571

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