PermutationMin

The smallest point $p$ moves; infinity for the identity.

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PermutationMin(p)The smallest point

p

moves; infinity for the identity.

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
Leading fixed points do not count: {1, 3, 2} has minimum 2
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 is fixed, so the smallest moved point is 2

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

Out

2

Known value · wolframscript 15.0

the one-line word $312$

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

Out

1

the one-line word $2413$

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

Out

1

Scope #

$(1\,5)(2\,3\,4)$

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

Out

1

Known value · wolframscript 15.0

Properties #

the identity moves nothing, so there is no smallest point, as Wolfram has it

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

Out

∞

Known value · wolframscript 15.0

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