partition

where n1, n2,…, nk are positive integers, and the order in which n1, n2,…, nk appear is unimportant. The number of partitions of n is denoted by p(n). For example, the partitions of 5 are

and hence p(5) =  7. The values of p(n) for small values of n are as follows:

Table of values of p(n)

The asymptotic approximation (see asymptotically equal)

for large n, was famously obtained by Hardy and Ramanujan in 1918.

Compare composition (of a number).

• principal value integral
• principle of conservation of energy
• principle of conservation of linear momentum
• principle of mathematical induction
• principle of moments
• principle of the excluded middle
• prior distribution
• prior probability
• prism
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• probability
• probability density function
• probability generating function
• probability mass function
• probability measure
• probability paper
• probability space
• probability vector
• probable error
• product
• product group
• product moment correlation coefficient
• product notation
• product of inertia