63 citations · 131 across the 29 of their papers we have counts for
29 papers
Promotion and rowmotion in rational Catalan combinatorics
Keiichi Shigechi
We study four bijections, which are promotion, evacuation, rowmotion, and rowvacuation, on generalized Dyck paths in rational Catalan combinatorics. We define the maps on generaliz…
Fuss--Catalan algebras on generalized Dyck paths via non-crossing partitions
Keiichi Shigechi
We study the Fuss--Catalan algebras, which are generalizations of the Temperley--Lieb algebra and act on generalized Dyck paths, through non-crossing partitions. First, the Temperl…
Jones--Wenzl projections of type and Dyck tilings
Keiichi Shigechi
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 coeffici…
Enumeration of labeled trees and Dyck tilings
Keiichi Shigechi
We study a partially ordered set of planar labeled rooted trees by use of combinatorial objects called Dyck tilings. A generating function of the poset is factorized when the minim…
Major Index on Catalan Combinatorics
Keiichi Shigechi
We study the two statistics, the inversion number and the major index, on Catalan combinatorial objects such as -Dyck paths, -Stirling permutations, non-crossing partitions,…
Jones--Wenzl projections and Dyck tilings: type and
Keiichi Shigechi
The Jones--Wenzl projections are a special class of elements of the Temperley--Lieb algebra. We prove that the coefficient appearing in the Jones--Wenzl projection is given by a ge…