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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 thepermutations in $[e, \omega]$ in the inversion order on $S_{n}$. In this paperwe show that $M_{\omega}$ is a $B_{2}$-free poset if and only if $\omega$ is a3412-3421-avoiding permutation.

A relation between the shape of a permutation and the shape of the base poset derived from the Lehmer codes