On refined enumerations of plane partitions of a given shape with bounded entries
Takuya Inoue · arXiv (Cornell University) · 2025
In this paper, we consider plane partitions $\text{PP}(λ; m)$ of a given shape $λ$, with entries at most $m$. We prove that the distributions of two statistics on $\text{PP}(λ; m)$ coincide: one is the number of rows containing $0$ and the other is the number of rows containing $m$. We also provide a bijective proof.