论文标题
部分可观测时空混沌系统的无模型预测
Computation of q-Binomial Coefficients with the $P(n,m)$ Integer Partition Function
论文作者
论文摘要
使用$ p（n，m）$，$ n $的整数分区数量恰好是$ m $零件，这是较早的论文的主题，$ p（n，m，p）$，$ n $ $ n $的数量$ n $的数量$ n $零件，每个零件最多$ p $，都可以计算为$ o（n^2）$ o（n^2）$ o（n^$ o o（n^of）$ o o（quffice of of o（n^of）。使用Q-binomial系数的定义，得出了Q-binomial系数的某些属性和$ p（n，m，p）$的某些属性。 Q-多性系数可以计算为Q-二项式系数的乘积。 $ q（n，m，p）$的公式，$ n $的整数分区的数量恰好是$ m $不同的零件，每个零件最多$ p $。一些用于整数分区数量的公式，每个部分在最小值和最大值之间。使用早期论文的计算机代数程序列出了计算机代数程序，以实现这些算法。
Using $P(n,m)$, the number of integer partitions of $n$ into exactly $m$ parts, which was the subject of an earlier paper, $P(n,m,p)$, the number of integer partitions of $n$ into exactly $m$ parts with each part at most $p$, can be computed in $O(n^2)$, and the q-binomial coefficient can be computed in $O(n^3)$. Using the definition of the q-binomial coefficient, some properties of the q-binomial coefficient and $P(n,m,p)$ are derived. The q-multinomial coefficient can be computed as a product of q-binomial coefficients. A formula for $Q(n,m,p)$, the number of integer partitions of $n$ into exactly $m$ distinct parts with each part at most $p$, is given. Some formulas for the number of integer partitions with each part between a minimum and a maximum are derived. A computer algebra program is listed implementing these algorithms using the computer algebra program of the earlier paper.
