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  • 1. Hultman, Axel
    et al.
    Linusson, Svante
    Shareshian, John
    Sjöstrand, Jonas
    Mälardalen University, School of Education, Culture and Communication.
    From Bruhat intervals to intersection lattices and a conjecture of Postnikov2009In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 116, no 3, p. 564-580Article in journal (Refereed)
  • 2.
    Sjöstrand, Jonas
    Royal Institute of Technology, Stockholm, Sweden.
    Bruhat intervals as rooks on skew Ferrers boards2007In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 114, no 7, p. 1182-1194Article in journal (Refereed)
    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.

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