3 papers
math.CO2026
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…
math.CO2025
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…
math.CO2024
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…