  We consider the generalized $k$-server problem on uniform metrics. We study
the power of memoryless algorithms and show tight bounds of $\Theta(k!)$ on
their competitive ratio. In particular we show that the \textit{Harmonic
Algorithm} achieves this competitive ratio and provide matching lower bounds.
This improves the $\approx 2^{2^k}$ doubly-exponential bound of Chiplunkar and
Vishwanathan for the more general setting of uniform metrics with different
weights.
