Year: 2021
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Shigechi, Keiichi
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3141904248