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arXiv · 2503.07957

On refined enumerations of plane partitions of a given shape with bounded entries

Takuya Inoue
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Abstract

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.

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Takuya Inoue. 2025-03-11. On refined enumerations of plane partitions of a given shape with bounded entries. https://arxiv.org/abs/2503.07957

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