  Permutation codes and multi-permutation codes have been widely considered due
to their various applications, especially in flash memory. In this paper, we
consider permutation codes and multi-permutation codes against a burst of
stable deletions. In particular, we propose a construction of permutation codes
correcting a burst stable deletion of length $s$, with redundancy $\log n+
2\log \log n+O(1)$. Compared to the previous known results, our improvement
relies on a different strategy to retrieve the missing symbol on the first row
of the array representation of a permutation. We also generalize our
constructions for multi-permutations and the variable length burst model.
Furthermore, we propose a linear-time encoder with optimal redundancy for
single stable deletion correcting permutation codes.
