Lattice Green's Functions of the Higher-Dimensional Face-Centered Cubic Lattices
Combinatorics
2013-03-12 v2 Symbolic Computation
Abstract
We study the face-centered cubic lattice (fcc) in up to six dimensions. In particular, we are concerned with lattice Green's functions (LGF) and return probabilities. Computer algebra techniques, such as the method of creative telescoping, are used for deriving an ODE for a given LGF. For the four- and five-dimensional fcc lattices, we give rigorous proofs of the ODEs that were conjectured by Guttmann and Broadhurst. Additionally, we find the ODE of the LGF of the six-dimensional fcc lattice, a result that was not believed to be achievable with current computer hardware.
Keywords
Cite
@article{arxiv.1108.2164,
title = {Lattice Green's Functions of the Higher-Dimensional Face-Centered Cubic Lattices},
author = {Christoph Koutschan},
journal= {arXiv preprint arXiv:1108.2164},
year = {2013}
}
Comments
16 pages, final version