On geometric constants for discrete Morrey spaces

In this note we prove that the $n$-th Von Neumann-Jordan constant and the $n$-th James constant for discrete Morrey spaces $\ell^p_q$ where $1\le p<q<\infty$ are both equal to $n$. This result tells us that the discrete Morrey spaces are not uniformly non-$\ell^1$, and hence they are not uniformly $n$-convex.