PermutationSupport

The points $p$ moves, in increasing order.

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PermutationSupport(p)The points

p

moves, in increasing order.

Typed signatures

Type	Package	Applies
`(permutation) -> list<integer>`	`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 has an empty support; the support's size is PermutationLength
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 #

$(1\,5)(2\,3\,4)$ moves all five points

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

Out

\bigl\lbrack1, 2, 3, 4, 5\bigr\rbrack

Known value · wolframscript 15.0

the one-line word $312$

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

Out

\bigl\lbrack1, 2, 3\bigr\rbrack

the one-line word $2413$

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

Out

\bigl\lbrack1, 2, 3, 4\bigr\rbrack

Scope #

1 and 4 are fixed

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

Out

\bigl\lbrack2, 3\bigr\rbrack

Known value · wolframscript 15.0

Properties #

the identity moves nothing

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

Out

\bigl\lbrack\bigr\rbrack

Known value · wolframscript 15.0

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