PermutationOrder

The order of p in the symmetric group — the lcm of its cycle lengths.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000058via Permutation✓Wolfram LanguagePermutationOrder✓

PermutationOrder(p)The order of p in the symmetric group — the lcm of its cycle lengths.

Typed signatures

Type	Package	Applies
`(permutation) -> number`	`combinatorics`	always

Domain: Permutation statistics

Details

Defined over Permutation as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
Takes a Permutation and nothing else — it reads values against their positions, or walks the orbits, so it needs the bijection. Applying it to a bare list is a type error, not a wrong answer.
Wolfram's PermutationOrder. The bare Order is Wolfram's canonical-ordering comparison Order[a, b], so this head replaces it. The old name is recorded in formerly but does not resolve: Order(p) is now Wolfram's Order.

Examples

Basic #

the one-line word $312$

\mathrm{PermutationOrder}({\operatorname{Permutation}}([3, 1, 2]))

Out

3

the one-line word $2413$

\mathrm{PermutationOrder}({\operatorname{Permutation}}([2, 4, 1, 3]))

Out

4

Properties #

FindStat's value for [1]

\mathrm{CombinatorialStat}({\operatorname{Permutation}}([1]), \text{PermutationOrder})

Out

1

Known value · FindStat St000058

FindStat's value for [1,2]

\mathrm{CombinatorialStat}({\operatorname{Permutation}}([1, 2]), \text{PermutationOrder})

Out

1

Known value · FindStat St000058

FindStat's value for [2,1]

\mathrm{CombinatorialStat}({\operatorname{Permutation}}([2, 1]), \text{PermutationOrder})

Out

2

Known value · FindStat St000058

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