Fungrim symbol: PartitionsP

Symbol: PartitionsP —

p(n)

— Integer partition function

p(n)

denotes the number of ways the integer

n

can be written as a sum of positive integers.

Domain	Codomain
$n \in \mathbb{Z}$	$p(n) \in \mathbb{Z}_{\ge 0}$
$n \in \mathbb{Z}_{\ge 0}$	$p(n) \in \mathbb{Z}_{\ge 1}$

Table data:

\left(P, Q\right)

such that

\left(P\right) \;\implies\; \left(Q\right)

Definitions:

Fungrim symbol	Notation	Short description
`PartitionsP`	$p(n)$	Integer partition function
`ZZ`	$\mathbb{Z}$	Integers
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("f5e153"),
    SymbolDefinition(PartitionsP, PartitionsP(n), "Integer partition function"),
    Description(PartitionsP(n), "denotes the number of ways the integer", n, "can be written as a sum of positive integers."),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(Element(n, ZZ), Element(PartitionsP(n), ZZGreaterEqual(0))), Tuple(Element(n, ZZGreaterEqual(0)), Element(PartitionsP(n), ZZGreaterEqual(1))))))

Topics using this symbol

The symbol PartitionsP appears in 3 topics:

Partition function (in 23 entries)
Integer sequences (in 1 entries)
Bell numbers (in 1 entries)

Entries using this symbol

The symbol PartitionsP appears in 24 entries: