  Two words have a reverse if they have the same pair of distinct letters on
the same pair of positions, but in reversed order. A set of words no two of
which have a reverse is said to be reverse-free. Let F(n,k) be the maximum size
of a reverse-free set of words from [n]^k where no letter repeats within a
word. We show the following lower and upper bounds in the case n >= k: F(n,k)
\in n^k k^{-k/2 + O(k/log k)}. As a consequence of the lower bound, a set of
n-permutations each two having a reverse has size at most n^{n/2 + O(n/log n)}.
