constrained partition function P | unrestricted partition function P

P(n), sometimes also denoted p(n), gives the number of ways of writing the integer n as a sum of positive integers, where the order of addends is not considered significant. By convention, partitions are usually ordered from largest to smallest. For example, since 4 can be written 4 | = | 4 | = | 3 + 1 | = | 2 + 2 | = | 2 + 1 + 1 | = | 1 + 1 + 1 + 1, it follows that P(4) = 5. P(n) is sometimes called the number of unrestricted partitions, and is implemented in the Wolfram Language as PartitionsP[n].

Alcuin's sequence | conjugate partition | Elder's theorem | Euler identity | Ferrers diagram | Göllnitz's theorem | partition | partition function P congruences | partition function Q | pentagonal number | pentagonal number theorem | plane partition | random partition | Rogers-Ramanujan identities | self-conjugate partition | Stanley's theorem | sum of squares function | tau function