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 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.
Keywords
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