Solid partition

In mathematics, solid partitions are natural generalizations of partitions and plane partitions defined by Percy Alexander MacMahon. 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

and

Let $p_3(n)$ denote the number of solid partitions of $n$ . As the definition of solid partitions involves three-dimensional arrays of numbers, they are also called three-dimensional partitions in notation where plane partitions are two-dimensional partitions and partitions are one-dimensional partitions. Solid partitions and their higher-dimensional generalizations are discussed in the book by Andrews.

单词	Solid partition
释义	Solid partition 英语百科 Solid partition In mathematics, solid partitions are natural generalizations of partitions and plane partitions defined by Percy Alexander MacMahon. 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 and Let $p_3(n)$ denote the number of solid partitions of $n$ . As the definition of solid partitions involves three-dimensional arrays of numbers, they are also called three-dimensional partitions in notation where plane partitions are two-dimensional partitions and partitions are one-dimensional partitions. Solid partitions and their higher-dimensional generalizations are discussed in the book by Andrews.
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