we consider permutations which are $1324$ and $\overline{2143}$ avoiding, where $\overline{2143}$ avoiding means that it is $2143$ avoiding with the additional bruhat restriction $\{2\leftrightarrow3\}$. in particular, for every permutation $\pi$ we will construct a linear map $l_\pi$ and a labeled graph $g_\pi$ and will show that the following three conditions are equivalent: $\pi$ is $1324$ and $\overline{2143}$ avoiding; $l_\pi$ is onto; $g_\pi$ is a forest. if time allows we will give a constructive proof showing that the $n$th catalan number gives a lower bound for the number of such permutations in $s_n$. \vskip .1in \noindent this answers a conjecture of woo and yong, which shows that such permutations characterize which schubert varieties are factorial.