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 $n$.
Categories: math.CO