  Sergey Kitaev has shown that the exponential generating function for
permutations avoiding the generalized pattern $\sigma$-$k$, where $\sigma$ is a
pattern without dashes and $k$ is one greater than the biggest element in
$\sigma$, is determined by the exponential generating function for permutations
avoiding $\sigma$.
  We show that this also holds for permutations avoiding all the generalized
patterns $\sigma_1$-$k_1$, $...$, $\sigma_n$-$k_n$, where $\sigma_1$, $...$,
$\sigma_n$ are patterns without dashes and $k_i$ is one greater than the
biggest element in $\sigma_i$. Similarly the exponential generating function
for permutations avoiding the partially ordered generalized patterns
$k_1$-$\sigma_1$-$k_1$, $...$, $k_n$-$\sigma_n$-$k_n$ can be determined from
the exponential generating function for permutations avoiding the generalized
patterns $\sigma_1$, $...$, $\sigma_n$, where $\sigma_1$, $...$, $\sigma_n$ are
patterns without dashes and $k_i$ is one greater than the largest element in
$\sigma_i$.
  Using this we construct a bijection between bicolored set partitions and
permutations avoiding the partially ordered generalized pattern 3-12-3 (that
is, permutations avoiding both the patterns 3-12-4 and 4-12-3). By using this
method twice, we find a closed formula for the exponential generating function
for permutations avoiding the partially ordered generalized pattern 3-121-3.
  Finally, we give a complete classification of when single partially ordered
generalized patterns have the same set of avoiders.
