Difference between revisions of "Partition"

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Let $n$ be an integer. Let $p(0)=1$ and let $p(n)=0$ for negative $n$. For positive $n$, the partition function $p(n)$ is the number of possible partitions of a number $n$ into sums of natural numbers. <br /><br />
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The partition function $p \colon \mathbb{Z}^+ \rightarrow \mathbb{Z}^+$ is defined so that $p(n)$ denotes the number of ways of writing $n$ as a sum of positive integers (without regarding order as important).
  
<strong>Example:</strong> We see that $p(4)=5$ because we can write
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=Properties=
$$\begin{array}{ll}
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4 &= 1+3 \\
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=References=
&= 1+1+2 \\
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Generating function for partition function}}: $24.2.1 \mathrm{I}.A.$
&= 1+1+1+1 \\
 
&= 2+2 \\
 
&= 0+4
 
\end{array}$$
 
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Revision as of 23:56, 25 June 2016

The partition function $p \colon \mathbb{Z}^+ \rightarrow \mathbb{Z}^+$ is defined so that $p(n)$ denotes the number of ways of writing $n$ as a sum of positive integers (without regarding order as important).

Properties

References