Fungrim symbol: StirlingCycle

Symbol: StirlingCycle —

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

— Unsigned Stirling number of the first 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
`StirlingCycle`	$\left[{n \atop k}\right]$	Unsigned Stirling number of the first kind
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("778fa2"),
    SymbolDefinition(StirlingCycle, StirlingCycle(n, k), "Unsigned Stirling number of the first 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(StirlingCycle(n, k), ZZGreaterEqual(0))))))

Topics using this symbol

The symbol StirlingCycle appears in 2 topics:

Stirling numbers (in 8 entries)
Lambert W-function (in 2 entries)

Entries using this symbol

The symbol StirlingCycle appears in 10 entries: