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

Gregory S. Warrington

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

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arxiv 1010.3961 v1 pith:Y5WKM5IX submitted 2010-10-19 math.CO math.RT

Gregory S. Warrington This is my paper · ORCID

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keywords classesequivalencekazhdan-lusztigvaluesattainedclasscoefficientscompute

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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 S_10 and S_11.

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Big data approach to Kazhdan-Lusztig polynomials
math.RT 2024-12 conditional novelty 6.0 of 10

Data on Kazhdan-Lusztig polynomials up to S_11 suggests superexponential growth of extremal coefficients, near-universal unimodality, and a conjectured closed family (1+v+...+v^l)^{k-1}.

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