Difference between revisions of "Partition"
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(Created page with "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 $n$ int...") |
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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 /> | 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 /> | ||
| − | <strong>Example:</ | + | <strong>Example:</strong> We see that $p(4)=5$ because we can write |
$$\begin{array}{ll} | $$\begin{array}{ll} | ||
4 &= 1+3 \\ | 4 &= 1+3 \\ | ||
Revision as of 07:56, 27 July 2014
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.
Example: We see that $p(4)=5$ because we can write $$\begin{array}{ll} 4 &= 1+3 \\ &= 1+1+2 \\ &= 1+1+1+1 \\ &= 2+2 \\ &= 0+4 \end{array}$$
