Fungrim entry: 32e430

Symbol: LandauG —

g(n)

— Landau's function

Landau's function

g(n)

gives the largest order of an element of the symmetric group

{S}_{n}

It can be defined arithmetically as the maximum least common multiple of the partitions of

n

, as in 7932c3.

The following table lists conditions such that LandauG(n) is defined in Fungrim.

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

Table data:

\left(P, Q\right)

such that

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

References:

https://oeis.org/A000793

Definitions:

Fungrim symbol	Notation	Short description
`LandauG`	$g(n)$	Landau's function
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("32e430"),
    SymbolDefinition(LandauG, LandauG(n), "Landau's function"),
    Description("Landau's function", LandauG(n), "gives the largest order of an element of the symmetric group", Subscript(S, n), "."),
    Description("It can be defined arithmetically as the maximum least common multiple of the partitions of", n, ", as in", EntryReference("7932c3"), "."),
    Description("The following table lists conditions such that", SourceForm(LandauG(n)), "is defined in Fungrim."),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(Element(n, ZZGreaterEqual(0)), Element(LandauG(n), ZZGreaterEqual(1))))),
    References("https://oeis.org/A000793"))

Topics using this entry

Landau's function