Generic asymptotics of resonance counting function for Schr\"odinger point interactions

We study the leading coefficient in the asymptotical formula $N (R) = \frac{W}{\pi} R + O (1)$, $R \to \infty$, for the resonance counting function $N (R)$ of Schr\"odinger Hamiltonians with point interactions. For such Hamiltonians, the Weyl-type and non-Weyl-type asymptotics of $N (R)$ was introduced recently in a paper by J. Lipovsk\'y and V. Lotoreichik (2017). In this note, we prove that the Weyl-type asymptotics is generic.