  We show that a monic polynomial in a discrete variable $n$, with coefficients
depending on time variables $t_1, t_2,...$ is a $\tau$-function for the
discrete Kadomtsev-Petviashvili hierarchy if and only if the motion of its
zeros is governed by a hierarchy of Ruijsenaars-Schneider systems. These
$\tau$-functions were considered in [12], where it was proved that they
parametrize rank one solutions to a difference-differential version of the
bispectral problem.
