Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Weak Bruhat Order and Separable Permutations   In this paper we consider the rank generating function of a separable
permutation $\pi$ in the weak Bruhat order on the two intervals $[\text{id},
\pi]$ and $[\pi, w_0]$, where $w_0 = n,(n-1),..., 1$. We show a surprising
result that the product of these two generating functions is the generating
function for the symmetric group with the weak order. We then obtain explicit
formulas for the rank generating functions on $[\text{id}, \pi]$ and $[\pi,
w_0]$, which leads to the rank-symmetry and unimodality of the two graded
posets.

17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an