Solid partition

Solid Partitions

Solid partitions are natural generalizations of partitions and plane partitions. A solid partition of $n$ is a three-dimensional array, $n_{i,j,k}$, of non-negative integers (the indices $i,\ j\ k\geq 1$) such that $\sum _{i,j,k}n_{i,j,k}=n$ and

$n_{i+1,j,k}\leq n_{i,j,k}\quad ,\quad n_{i,j+1,k}\leq n_{i,j,k}\quad ,\quad n_{i,j,k+1}\leq n_{i,j,k}\quad ,\quad \forall i,\ j\mathrm {and} k\ .$

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