Lattice Green's Functions of the Higher-Dimensional Face-Centered Cubic Lattices

Details Lattice Green's Functions of the Higher-Dimensional Face-Centered Cubic Lattices Lattice Green's Functions of the Higher-Dimensional Face-Centered Cubic Lattices

2011-08-10

arxiv.org/abs/1108.2164v1

Mathematics

Combinatorics

14 pages

Scientific paper

We study the lattice Green's functions of the face-centered cubic lattice (fcc) in up to six dimensions. We give computer algebra proofs of results that were conjectured by Guttmann and Broadhurst for the four- and five-dimensional fcc lattices. Additionally we derive a differential equation for the lattice Green's function of the six-dimensional fcc lattice, a result that was not believed to be achievable with current computer hardware.

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