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 ${\mathrm{\ell }}_q^p$ where $1\le p<q<\infty$arebothequalto$n$. This result tells us that the discrete Morrey spaces are not uniformly non-${\mathrm{\ell }}^1$, and hence they are not uniformly $n$-convex.