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Path representation of maximal parabolic Kazhdan-Lusztig polynomials

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arxiv 1001.1080 v3 pith:ILXGWQZ4 submitted 2010-01-07 math.CO math-phmath.MP

K. Shigechi , P. Zinn-Justin This is my paper · ORCID
classification math.COmath-phmath.MP
keywords maximalparabolicpolynomialsrulescasecertaincomparecomputation
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We provide simple rules for the computation of Kazhdan--Lusztig polynomials in the maximal parabolic case. They are obtained by filling regions delimited by paths with "Dyck strips" obeying certain rules. We compare our results with those of Lascoux and Sch\"utzenberger.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Fuss--Catalan algebras on generalized Dyck paths via non-crossing partitions

    math.CO 2025-07 conditional novelty 6.0 of 10

    Fuss-Catalan algebras and their one- and two-boundary versions are realized on increasing chains of non-crossing partitions, with a new r=2 reflection equation solution.

  2. Jones--Wenzl projections of type $D$ and Dyck tilings

    math.CO 2024-12 conditional novelty 6.0 of 10

    Coefficients of the type D Jones-Wenzl projection are expressed as generating functions over Dyck tilings decorated with bi-colored vertical Hermite histories, for both even and odd dot cases.

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