Jones--Wenzl projections of type D and Dyck tilings
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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