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arXiv · 2402.00660

A note on the number of plane partitions and $r$-component multipartitions of $n$

Mircea Cimpoeas·Alexandra Teodor
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Abstract

Using elementary methods, we prove new formulas for $\operatorname{pp}(n)$, the number of plane partitions of $n$, $\operatorname{pp}_r(n)$, the number of plane partitions of $n$ with at most $r$ rows, $\operatorname{pp}^s(n)$, the number of strict plane partitions of $n$ and $\operatorname{pp}^{so}(n)$, the number of symmetric plane partitions of $n$. Also, we give new formulas for $P_r(n)$, the number of $r$-component multipartitions of $n$.

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Mircea Cimpoeas, Alexandra Teodor. 2024-02-01. A note on the number of plane partitions and $r$-component multipartitions of $n$. https://arxiv.org/abs/2402.00660

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