 NumberTheory/Landau - Help

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NumberTheory

 Landau
 compute the Landau g function

 Calling Sequence Landau(n)

Parameters

 n - a positive integer

Description

 • The Landau function g(n) is defined to be the largest order of a permutation of degree n, where n is a positive integer.
 • The Landau(n) command computes the value of g(n).

Examples

 > $\mathrm{with}\left(\mathrm{NumberTheory}\right):$
 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $\mathrm{Landau}\left(3\right)$
 ${3}$ (1)
 > $\mathrm{max}\left(\mathrm{map}\left(\mathrm{PermOrder},\mathrm{Elements}\left(\mathrm{Symm}\left(3\right)\right)\right)\right)$
 ${3}$ (2)
 > $\mathrm{Landau}\left(10\right)$
 ${30}$ (3)
 > $\mathrm{Landau}\left(100\right)$
 ${232792560}$ (4)

Compatibility

 • The NumberTheory[Landau] command was introduced in Maple 2016.
 • For more information on Maple 2016 changes, see Updates in Maple 2016.

 See Also