Point Counts of D_k and Some A_k and E_k Integer Lattices Inside Hypercubes

Details Point Counts of D_k and Some A_k and E_k Integer Lattices Inside Hypercubes Point Counts of D_k and Some A_k and E_k Integer Lattices Inside Hypercubes

2010-02-19

arxiv.org/abs/1002.3844v2

Mathematics

Geometric Topology

Merged chapters 9 and 10, and added Table 5 and Conjecture 2.

Scientific paper

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.

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