Coffey, Mark W.; Allen, Grant Eigenvalue degeneracy relations for a fully connected isotropic spin network. (English) Zbl 1226.81035 J. Phys. A, Math. Theor. 44, No. 39, Article ID 395303, 21 p. (2011). Summary: We present and prove identities for the eigenvalue degeneracy of a fully connected spin network with isotropic spin coupling. Such a network has application to quantum information processing, especially for solid-state implementations, and in fact the qubit case with anisotropic coupling has been recently realized. One set of proofs and other relations for the case of qubits is given in the context of hypergeometric summation. We then generalize to arbitrary spin, using combinatorial arguments. MSC: 81P45 Quantum information, communication, networks (quantum-theoretic aspects) 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 34B45 Boundary value problems on graphs and networks for ordinary differential equations 81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics PDFBibTeX XMLCite \textit{M. W. Coffey} and \textit{G. Allen}, J. Phys. A, Math. Theor. 44, No. 39, Article ID 395303, 21 p. (2011; Zbl 1226.81035) Full Text: DOI