2021/04/07 by Shigechi, Keiichi
#Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2104.03085
We introduce rational Dyck tilings, or (a,b)-Dyck tilings, and study them by the decomposition into (1,1)-Dyck tilings. This decomposition allows us to make use of combinatorial models for (1,1)-Dyck tilings such as the Hermite history and the Dyck tiling strip bijection. Together with b-Stirling permutations associated to the rational Dyck tilings, we obtain a correspondence between an (a,b)-Dyck tiling and a tuple of ab (1,1)-Dyck tilings.