Equivalence classes for the mu-coefficient of Kazhdan-Lusztig polynomials in S_n

2010/10/19 by Gregory S. Warrington, Warrington, Gregory S.
Mathematics · #Advanced Combinatorial Mathematics #Advanced Algebra and Geometry #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1010.3961

Abstract

We study equivalence classes relating to the Kazhdan-Lusztig mu(x,w) coefficients in order to help explain the scarcity of distinct values. Each class is conjectured to contain a "crosshatch" pair. We also compute the values attained by mu(x,w) for the permutation groups S₁0 and S₁1.

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• The leading coefficient of certain Kazhdan-Lusztig polynomials of the permutation group S_n
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• Two formulae for inverse Kazhdan-Lusztig polynomials in S_n