The point-and-line case of the HRT conjecture

The linear independence of time-frequency shifts of a function in $L^2(\mathbb R)$ is studied for a special configuration of points used to generate those shifts, that is, when all these points except one are collinear (the point-and-line case). The linear independence of time-frequency shifts is reformulated in this case in a more accessible form. This reformulation is used to confirm the linear independence of time-frequency shifts in a certain subcase of the general point-and-line case.