Computing hypermatrix spectra with the Poisson product formula

Abstract

We compute the spectrum of the ‘all ones’ hypermatrix using the Poisson product formula. This computation includes a complete description of the eigenvalues’ multiplicities, a seemingly elusive aspect of the spectral theory of tensors. We also give a distributional picture of the spectrum as a point-set in the complex plane. Finally, we use the technique to analyse the spectrum of ‘sunflower hypergraphs’, a class that has played a prominent role in extremal hypergraph theory.