Does there exist an explicit criterion (or a good sufficient condition) for proving that a Vandemonde matrix:
$$\left[ \begin{array}{llll}1 & x_1 &\dots& x_1^{n-1}\\ 1 & x_2 &\dots& x_2^{n-1}\\&&\vdots&\\ 1& x_n &\dots& x_n^{n-1}\end{array}\right]$$
has nonzero permanent? ($x_1,\dots,x_n$ are complex numbers) I'm especially interested in the case where $x_i$'s are roots of unity.