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

Abstract

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.

arXiv comment8 pages, 3 figures

References in corpus (1)

• A refinement of weak order intervals into distributive lattices