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.
| Original language | English |
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| Number of pages | 14 |
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| Publication status | Published - 2011 |
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| Name | arXiv.org |
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| No. | 1108.2164 |
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- 101001 Algebra
- 101002 Analysis
- 101 Mathematics
- 102 Computer Sciences
- 102011 Formal languages
- 101009 Geometry
- 101013 Mathematical logic
- 101020 Technical mathematics
- 101025 Number theory
- 101012 Combinatorics
- 101005 Computer algebra
- 101006 Differential geometry
- 101003 Applied geometry
- 102025 Distributed systems
- Computation in Informatics and Mathematics