Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bruhat intervals as rooks on skew Ferrers boards   We characterise the permutations pi such that the elements in the closed
lower Bruhat interval [id,pi] of the symmetric group correspond to non-taking
rook configurations on a skew Ferrers board. It turns out that these are
exactly the permutations pi such that [id,pi] corresponds to a flag manifold
defined by inclusions, studied by Gasharov and Reiner.
  Our characterisation connects the Poincare polynomials (rank-generating
function) of Bruhat intervals with q-rook polynomials, and we are able to
compute the Poincare polynomial of some particularly interesting intervals in
the finite Weyl groups A_n and B_n. The expressions involve q-Stirling numbers
of the second kind.
  As a by-product of our method, we present a new Stirling number identity
connected to both Bruhat intervals and the poly-Bernoulli numbers defined by
Kaneko.

8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph