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

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

2011-11-14

arxiv.org/abs/1111.3094v1

Mathematics

Combinatorics

8 pages, 3 figures

Scientific paper

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.

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