  In the rank modulation scheme for flash memories, permutation codes have been
studied. In this paper, we study perfect permutation codes in $S_n$, the set of
all permutations on $n$ elements, under the Kendall \tau-Metric. We answer one
open problem proposed by Buzaglo and Etzion. That is, proving the nonexistence
of perfect codes in $S_n$, under the Kendall \tau-metric, for more values of
$n$. Specifically, we present the recursive formulas for the size of a ball
with radius $r$ in $S_n$ under the Kendall \tau-metric. Further, We prove that
there are no perfect $t$-error-correcting codes in $S_n$ under the Kendall
$\tau$-metric for some $n$ and $t$=2,3,4,or 5.
