#### Interlacing Suleĭmanova spectra

A set of real numbers $\{\lambda_1, \dots, \lambda_n \}$, $n \geq 1$, is called a Suleĭmanova spectrum if it contains exactly one positive value and $\sum_{i=1}^n \lambda_i \geq 0$. (It is well-known that any such set is the spectrum of an entry-wise $n$-by-$n$ nonnegative mat...