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

Combinatorics 2024-12-24 v1 Mathematical Physics math.MP Quantum Algebra Representation Theory

Abstract

We study the relation between a coefficient of an element of the Jones--Wenzl projection in the Temperley--Lieb algebra of type DD 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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Cite

@article{arxiv.2412.16966,
  title  = {Jones--Wenzl projections of type $D$ and Dyck tilings},
  author = {Keiichi Shigechi},
  journal= {arXiv preprint arXiv:2412.16966},
  year   = {2024}
}

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30 pages