  For a permutation $\omega \in S_{n}$ Denoncourt constructed a poset
$M_{\omega}$ which is the set of join-irreducibles of the Lehmer codes of the
permutations in $[e, \omega]$ in the inversion order on $S_{n}$. In this paper
we show that $M_{\omega}$ is a $B_{2}$-free poset if and only if $\omega$ is a
3412-3421-avoiding permutation.
