Fungrim entry: 778fa2

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 entry

Stirling numbers

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC