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Jones--Wenzl projections and Dyck tilings: type $A$ and $B$

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arxiv 2402.09887 v1 pith:OS4LMYM4 submitted 2024-02-15 math.CO cond-mat.stat-mechmath-phmath.MPmath.QA

Keiichi Shigechi This is my paper · ORCID
classification math.COcond-mat.stat-mechmath-phmath.MPmath.QA
keywords jones--wenzldyckprojectionstilingstypealgebraappearingcalled
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abstract

The Jones--Wenzl projections are a special class of elements of the Temperley--Lieb algebra. We prove that the coefficient appearing in the Jones--Wenzl projection is given by a generating function of combinatorial objects, called Dyck tilings. We also show that this correspondence holds for type $B$ case.

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Cited by 1 Pith paper

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  1. 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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