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Bruhat intervals as rooks on skew Ferrers boards
Royal Institute of Technology, Stockholm, Sweden.
2007 (English)In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 114, no 7, p. 1182-1194Article in journal (Refereed) Published
Abstract [en]

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. (C) 2007 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
2007. Vol. 114, no 7, p. 1182-1194
National Category
Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-4947DOI: 10.1016/j.jcta.2007.01.001ISI: 000250062100002Scopus ID: 2-s2.0-34547141681OAI: oai:DiVA.org:mdh-4947DiVA, id: diva2:159705
Available from: 2009-02-09 Created: 2009-02-09 Last updated: 2017-12-14Bibliographically approved

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