Fungrim symbol: StirlingS2

Symbol: StirlingS2 —

\left\{{n \atop k}\right\}

— Stirling number of the second kind

Domain	Codomain
$n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}$	$\left\{{n \atop k}\right\} \in \mathbb{Z}_{\ge 0}$

Table data:

\left(P, Q\right)

such that

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

Definitions:

Fungrim symbol	Notation	Short description
`StirlingS2`	$\left\{{n \atop k}\right\}$	Stirling number of the second kind
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("4c6c43"),
    SymbolDefinition(StirlingS2, StirlingS2(n, k), "Stirling number of the second kind"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(And(Element(n, ZZGreaterEqual(0)), Element(k, ZZGreaterEqual(0))), Element(StirlingS2(n, k), ZZGreaterEqual(0))))))

Topics using this symbol

The symbol StirlingS2 appears in 2 topics:

Stirling numbers (in 7 entries)
Bell numbers (in 1 entries)

Entries using this symbol

The symbol StirlingS2 appears in 8 entries: