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.
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Received May 13, 2005
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Incitti, F. Permutation Diagrams, Fixed Points and Kazhdan-Lusztig R-Polynomials. Ann. Comb. 10, 369–387 (2006). https://doi.org/10.1007/s00026-006-0294-6
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DOI: https://doi.org/10.1007/s00026-006-0294-6