Point Counts of D_k and Some A_k and E_k Integer Lattices Inside Hypercubes
Geometric Topology
2010-04-22 v2
Abstract
Regular integer lattices are characterized by k unit vectors that build up their generator matrices. These have rank k for D-lattices, and are rank-deficient for A-lattices, for E_6 and E_7. We count lattice points inside hypercubes centered at the origin for all three types, as if classified by maximum infinity norm in the host lattice. The results assume polynomial format as a function of the hypercube edge length.
Keywords
Cite
@article{arxiv.1002.3844,
title = {Point Counts of D_k and Some A_k and E_k Integer Lattices Inside Hypercubes},
author = {Richard J. Mathar},
journal= {arXiv preprint arXiv:1002.3844},
year = {2010}
}
Comments
Merged chapters 9 and 10, and added Table 5 and Conjecture 2.