Our papers are the official record of our discoveries. They allow others to build on and apply our work. Each paper is the result of many months of research, so we make a special effort to make them clear, beautiful and inspirational, and publish them in leading journals.
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Graph theory
Hypercube eigenvalues
Hamming balls, subgraphs of the hypercube, maximise the graph’s largest eigenvalue exactly when the dimension of the cube is large enough.
Graph theory
Eigenvalues of neutral networks
The principal eigenvalue of small neutral networks determines their robustness, and is bounded by the logarithm of the number of vertices.
Graph theory
Erdős-Ko-Rado theorem analogue
A random analogue of the Erdős-Ko-Rado theorem sheds light on its stability in an area of parameter space which has not yet been explored.
Statistical physics
Spin systems on Bethe lattices
Exact equations for the thermodynamic quantities of lattices made of d-dimensional hypercubes are obtainable with the Bethe-Peierls approach.