  The HRT (Heil-Ramanathan-Topiwala) posits the linear independence of any set
of nonzero square-integrable vectors obtained from a single nonzero vector $f$
by applying a finite set of time-frequency shift operators. In this short note,
we present findings centered on the zero set of the Zak transform of $f$, and a
distinct arrangement involving a finite set of $N$ points on an integer lattice
in the time-frequency plane, excluding a specific point.
