  Highly frustrated lattices yield a completely flat lowest single-electron
band. Remarkably, exact many-body ground states can be constructed for the
repulsive Hubbard model and the t-J model by filling this flat band with
localized electron states. This construction leads to a macroscopic
ground-state degeneracy. We discuss how to compute these ground-state
degeneracies for a certain class of models, including in particular the
sawtooth chain. Furthermore, we discuss generic consequences for
low-temperature thermodynamic properties, like the appearance of a
low-temperature peak in the specific heat. Finally, we present complementary
numerical results obtained by exact diagonalization.
