Q-Counting rook configurations and a formula of Frobenius
Journal of Combinatorial Theory Series A
Rook placements and cellular decomposition of partition varieties
Discrete Mathematics
Rook polynomials to and from permanents
Discrete Mathematics - The 2000 Com2MaC conference on association schemes, codes and designs
Bruhat intervals of length 4 in Weyl groups
Journal of Combinatorial Theory Series A
More on the combinatorial invariance of Kazhdan--Lusztig polynomials
Journal of Combinatorial Theory Series A
Bruhat order, smooth Schubert varieties, and hyperplane arrangements
Journal of Combinatorial Theory Series A
From Bruhat intervals to intersection lattices and a conjecture of Postnikov
Journal of Combinatorial Theory Series A
Pattern avoidance and Boolean elements in the Bruhat order on involutions
Journal of Algebraic Combinatorics: An International Journal
Inversion arrangements and Bruhat intervals
Journal of Combinatorial Theory Series A
Enumerating indices of Schubert varieties defined by inclusions
Journal of Combinatorial Theory Series A
Journal of Algebraic Combinatorics: An International Journal
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We characterise the permutations @p such that the elements in the closed lower Bruhat interval [id,@p] of the symmetric group correspond to non-taking rook configurations on a skew Ferrers board. It turns out that these are exactly the permutations @p such that [id,@p] 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, and for the group A"n putting q=1 yields the poly-Bernoulli numbers defined by Kaneko.