2024/12/22 by Shigechi, Keiichi
#Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2412.16966
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.