Bruhat intervals as rooks on skew Ferrers boards
2007 (English)In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 114, no 7, 1182-1198 p.Article in journal (Refereed) Published
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 connect, 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 An and B, The expressions involve q-Stirling numbers of the second kind, and for the group A, putting q = 1 yields the poly-Bernoulli numbers defined by Kaneko.
Place, publisher, year, edition, pages
2007. Vol. 114, no 7, 1182-1198 p.
Bruhat order; Coxeter group; Partition variety; Poincaré polynomial; Rook polynomial; Weyl group
IdentifiersURN: urn:nbn:se:kth:diva-6862DOI: 10.1016/j.jcta.2007.01.001ISI: 000250062100002ScopusID: 2-s2.0-34547141681OAI: oai:DiVA.org:kth-6862DiVA: diva2:11691
QC 20100818. Uppdaterad från Accepted till Published 20100818.2007-03-092007-03-092010-08-18Bibliographically approved