  Using the example of the sawtooth chain, we argue that the t-J model shares
important features with the Hubbard model on highly frustrated lattices. The
lowest single-fermion band is completely flat (for a specific choice of the
hopping parameters $t_{i,j}$ in the case of the sawtooth chain), giving rise to
single-particle excitations which can be localized in real space. These
localized excitations do not interact for sufficient spatial separations such
that exact many-electron states can also be constructed. Furthermore, all these
excitations acquire zero energy for a suitable choice of the chemical potential
$\mu$. This leads to: (i) a jump in the particle density at zero temperature,
(ii) a finite zero-temperature entropy, (iii) a ferromagnetic ground state with
a charge gap when the flat band is fully occupied and (iv) unusually large
temperature variations when $\mu$ is varied adiabatically at finite
temperature.
