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arXiv · 2412.16966

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

Keiichi Shigechi
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Abstract

We study the relation between a coefficient of an element of the Jones--Wenzl projection in the Temperley--Lieb algebra of type $D$ and an enumeration of Dyck tilings. The coefficient can be non-recursively expressed as an enumerative generating function of Dyck tilings by considering the generalized Hermite histories, which we call bi-colored vertical Hermite histories, on the tilings.

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Keiichi Shigechi. 2024-12-22. Jones--Wenzl projections of type $D$ and Dyck tilings. https://arxiv.org/abs/2412.16966

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