Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A relation between the shape of a permutation and the shape of the base
  poset derived from the Lehmer codes   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.

19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph