PermutationLength

The number of points $p$ moves.

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PermutationLength(p)The number of points

p

moves.

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.
Wolfram's Cycles input is not read here: wrap a one-line word in Permutation, or turn Cycles into one with PermutationList first
The identity moves nothing, so its length is 0; a $k$ -cycle has length $k$ (fixed points do not count)
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.

Examples

Basic #

all three points move

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

Out

3

Known value · wolframscript 15.0

the one-line word $312$

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

Out

3

the one-line word $2413$

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

Out

4

Scope #

only 2 and 3 move

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

Out

2

Known value · wolframscript 15.0

the cycles $(1\,5)(2\,3\,4)$ move five points

\mathrm{PermutationLength}({\operatorname{Permutation}}([5, 3, 4, 2, 1]))

Out

5

Known value · wolframscript 15.0

Properties #

the identity moves nothing

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

Out

0

Known value · wolframscript 15.0

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