  We study one-dimensional strongly interacting Bose-Fermi mixtures by both the
exact Bethe-ansatz method and variational perturbation theory within the
degenerate ground state subspace of the system in the infinitely repulsive
limit. Based on the exact solution of the one-dimensional Bose-Fermi gas with
equal boson-boson and boson-fermion interaction strengths, we demonstrate that
the ground state energy is degenerate for different Bose-Fermi configurations
and the degeneracy is lifted when the interaction deviates the infinitely
interacting limit. We then show that the ground properties in the strongly
interacting regime can be well characterized by using the variational
perturbation method within the degenerate ground state subspace, which can be
applied to deal with more general cases with anisotropic interactions and in
external traps. Our results indicate that the total ground-state density
profile in the strongly repulsive regime behaves like the polarized
noninteracting fermions, whereas the density distributions of bosons and
fermions display different properties for different Bose-Fermi configurations
and are sensitive to the anisotropy of interactions.
