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Permutation Diagrams, Fixed Points and Kazhdan-Lusztig R-Polynomials
Federico Incitti
Department of Mathematics, Royal Institute of Technology, Lindstedts väg 25, 10044 Stockholm, Sweden
incitti@math.kth.se
Annals of Combinatorics 10 (3) p. 369-387 September, 2006
AMS Subject Classification: 05E15, 20F55
Abstract:
In this paper, we give an algorithm for computing the Kazhdan-Lusztig, R-polynomials in the symmetric group. The algorithm is described in terms of permutation diagrams. In particular we focus on how the computation of the polynomial is affected by certain fixed points. As a consequence of our methods, we obtain explicit formulas for the R-polynomials associated with some general classes of intervals, generalizing results of Brenti and Pagliacci.
Keywords: permutation diagram, fixed point, Bruhat order, Kazhdan-Lusztig polynomial, R-polynomial

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