  The validity of the Luttinger sum rule is considered for finite systems of
interacting electrons, where the Fermi volume is determined by location of
zeroes of Green's function. It is shown that the sum rule in the paramagnetic
state is evidently violated within the planar t-J model at low doping while for
the related Hubbard model, even in the presence of next-nearest-neighbor
hopping, no clearcut exception is found.
