Lattice Green's Functions of the Higher-Dimensional Face-Centered Cubic Lattices
Sprache des Vortragstitels:
CSASC (Joint Mathematical Conference of the Austrian Mathematical Society together with the Catalan, Czech, Slovak, and Slovenian Mathematical Societies, Minisymposium "Combinatorics and Graph Theory")
Sprache des Tagungstitel:
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 six-dimensional fcc lattice, a result that was not believed to be achievable with current computer hardware.