论文标题
$ p（n，m）$的计算，$ n $的整数分区的数量恰好$ m $零件
Computation of $P(n,m)$, the Number of Integer Partitions of $n$ into Exactly $m$ Parts
论文作者
论文摘要
描述了两种用于计算$ p（n，m）$的算法，这些算法被描述为$ n $恰好$ m $零件的整数分区的数量，并结合了这两种算法的组合，结果算法为$ O（n^{3/2}）$。第二个算法使用$ p（n）$的列表，即$ n $的整数分区的数量，该$ n $被缓存，因此只需计算一次。计算此列表也为$ O（n^{3/2}）$。使用这些算法，$ q（n，m）$，$ n $的整数分区的数量恰好是$ m $不同的零件，以及$ q（n）$的列表，可以以$ o（n^{3/2}）$计算的$ n $的整数分区数量。 $ p（n，1）的列表。p（n，n）$和$ p（m，m）.. p（n，m）$可以以$ o（n^2）$计算。列出了实施这些算法的计算机代数程序，并提供了该程序的某些时间。
Two algorithms for computing $P(n,m)$, the number of integer partitions of $n$ into exactly $m$ parts, are described, and using a combination of these two algorithms, the resulting algorithm is $O(n^{3/2})$. The second algorithm uses a list of $P(n)$, the number of integer partitions of $n$, which is cached and therefore needs to be computed only once. Computing this list is also $O(n^{3/2})$. With these algorithms also $Q(n,m)$, the number of integer partitions of $n$ into exactly $m$ distinct parts, and a list of $Q(n)$, the number of integer partitions of $n$ into distinct parts, can be computed in $O(n^{3/2})$. A list of $P(n,1)..P(n,n)$ and $P(m,m)..P(n,m)$ can be computed in $O(n^2)$. A computer algebra program is listed implementing these algorithms, and some timings of this program are provided.
