  We study the effects of hole doping on one-dimensional Mott insulators with
orbital degrees of freedom. We describe the system in terms of a generalized
t-J model. At a specific point in parameter space the model becomes integrable
in analogy to the one-band supersymmetric t-J model. We use the Bethe ansatz to
derive a set of nonlinear integral equations which allow us to study the
thermodynamics exactly. Moving away from this special point in parameter space
we use the density-matrix renormalization group applied to transfer matrices to
study the evolution of various phases of the undoped system with doping and
temperature. Finally, we study a one-dimensional version of a realistic model
for cubic titanates which includes the anisotropy of the orbital sector due to
Hund's coupling. We find a transition from a phase with antiferromagnetically
correlated spins to a phase where the spins are fully ferromagnetically
polarized, a strong tendency towards phase separation at large Hund's coupling,
as well as the possibility of an instability towards triplet superconductivity.
