1 Introduction
For each \(r \ge 2\), there exists \(\delta = \delta (r) {\gt} 0\) such that
\begin{equation*} R_r(k) \le e^{-\delta k} r^{rk} \end{equation*}
for all sufficiently large \(k \in \mathbb {N}\).
For each \(r \ge 2\), there exists \(\delta = \delta (r) {\gt} 0\) such that
for all sufficiently large \(k \in \mathbb {N}\).