  Based on a multi-phase transport model for relativistic heavy-ion collisions,
effects of the parton scatterings on the production of strangeness in
relativistic heavy-ion collisions are studied. It is found that the
distributions of strange quark and strange baryon, especially for the double
strangeness $\Xi^{-}$, are significantly affected by the parton scatterings in
heavy-ion collisions below $\sqrt{s_{NN}}\sim$ 10 GeV. Given parton scatterings
as a signal of the formation of quark matter, the transverse momentum
distribution of the ratio of single and double strangeness
$(\Lambda+\Sigma^{0})/\Xi^{-}$ produced in heavy-ion collisions may serve as a
potential probe of the emergence of quark matter, or equivalently, the
occurrence of hadron-quark phase transition in relativistic heavy-ion
collisions.
