Partition function (number theory): Difference between revisions
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In [[number theory]] the '''partition function''' ''p''(''n'') counts the number of [[partition]]s of a positive integer ''n'', that is, the number of ways of expressing ''n'' as a sum of positive integers (where order is not significant). | In [[number theory]] the '''partition function''' ''p''(''n'') counts the number of [[partition]]s of a positive integer ''n'', that is, the number of ways of expressing ''n'' as a sum of positive integers (where order is not significant). | ||
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The partition function satisfies an asymptotic relation | The partition function satisfies an asymptotic relation | ||
:<math> p(n) \sim \frac{\exp\left(\pi\sqrt{2/3}\sqrt n\right)}{4n\sqrt3} .</math> | :<math> p(n) \sim \frac{\exp\left(\pi\sqrt{2/3}\sqrt n\right)}{4n\sqrt3} .</math>[[Category:Suggestion Bot Tag]] | ||
Latest revision as of 16:00, 1 October 2024
In number theory the partition function p(n) counts the number of partitions of a positive integer n, that is, the number of ways of expressing n as a sum of positive integers (where order is not significant).
Thus p(3) = 3, since the number 3 has 3 partitions:
- 3
- 2+1
- 1+1+1
Properties
The partition function satisfies an asymptotic relation
