  The HRT (Heil-Ramanathan-Topiwala) conjecture stipulates that the set of any
finitely many time-frequency shifts of a non-zero square Lebesgue integrable
function is linearly independent. The present work settles two special cases of
this conjecture, namely, the cases where the set of time-frequency shifts has
cardinality $N+1$ such that either $N$ of the points lie on some integer
lattice and the last point is arbitrary, or $N$ of the points are on a line,
while the last point does not belong this line. In both cases, we prove that
the HRT conjecture holds appealing mainly to various forms of the ergodic
theorem. We note that, in recent years, the latter case has been the subject of
many investigations -- notably, the subcase where $N=3$ -- and our work
completely resolves it.
