Sylvester-Kac matrices with quadratic spectra: a comprehensive note (Q6631617)

Sylvester-Kac matrices are tridiagonal integral matrices whose eigenvalues are integers or express some kind of regularity. Such matrices with spectra having some type of quadratic form have widely been studied in the literature. The authors review these results. Using a lower triangular matrix based on Pascal's triangle, they also present a unified approach to them. Finally, they give a comprehensive bibliography on the history and recent development of this topic.