Partition function (number theory)
Jump to navigation
Jump to search
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
References
- Tom M. Apostol (1990). Modular functions and Dirichlet Series in Number Theory, 2nd ed. Springer-Verlag, 94-112. ISBN 0-387-97127-0.
- G.H. Hardy; E. M. Wright (2008). An Introduction to the Theory of Numbers, 6th ed.. Oxford University Press, 361-392. ISBN 0-19-921986-5.