Coweight lattice $A^*_n$ and lattice simplices
Combinatorics
2020-03-24 v1 Metric Geometry
Abstract
There exist as many index- sublattices of the hexagonal lattice up to isometry as there exist lattice triangles with normalized volume up to unimodular equivalence, which can be explained using orbifolds. In dimension 3, it was noted that the number of sublattices of the fcc and the bcc lattices and the number of lattice tetrahedra all seem to be the same. We provide a bijection between the sublattices of the coweight lattice and the -dimensional lattice simplices. It explains, proves, and generalizes the observed coincidences to arbitrary dimension.
Keywords
Cite
@article{arxiv.2003.10251,
title = {Coweight lattice $A^*_n$ and lattice simplices},
author = {Andrey Zabolotskiy},
journal= {arXiv preprint arXiv:2003.10251},
year = {2020}
}