Fungrim entry: f5e153

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))))))

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2021-03-15 19:12:00.328586 UTC