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

Abstract

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

13 pages