- FindStat

Identifier

Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St000001: Permutations ⟶ ℤ

Values

[1] => [1] => 1

[1,2] => [1,2] => 1

[2,1] => [1,2] => 1

[1,2,3] => [1,2,3] => 1

[1,3,2] => [1,2,3] => 1

[2,1,3] => [1,2,3] => 1

[2,3,1] => [1,2,3] => 1

[3,1,2] => [1,3,2] => 1

[3,2,1] => [1,3,2] => 1

[1,2,3,4] => [1,2,3,4] => 1

[1,2,4,3] => [1,2,3,4] => 1

[1,3,2,4] => [1,2,3,4] => 1

[1,3,4,2] => [1,2,3,4] => 1

[1,4,2,3] => [1,2,4,3] => 1

[1,4,3,2] => [1,2,4,3] => 1

[2,1,3,4] => [1,2,3,4] => 1

[2,1,4,3] => [1,2,3,4] => 1

[2,3,1,4] => [1,2,3,4] => 1

[2,3,4,1] => [1,2,3,4] => 1

[2,4,1,3] => [1,2,4,3] => 1

[2,4,3,1] => [1,2,4,3] => 1

[3,1,2,4] => [1,3,2,4] => 1

[3,1,4,2] => [1,3,4,2] => 1

[3,2,1,4] => [1,3,2,4] => 1

[3,2,4,1] => [1,3,4,2] => 1

[3,4,1,2] => [1,3,2,4] => 1

[3,4,2,1] => [1,3,2,4] => 1

[4,1,2,3] => [1,4,3,2] => 2

[4,1,3,2] => [1,4,2,3] => 1

[4,2,1,3] => [1,4,3,2] => 2

[4,2,3,1] => [1,4,2,3] => 1

[4,3,1,2] => [1,4,2,3] => 1

[4,3,2,1] => [1,4,2,3] => 1

[1,2,3,4,5] => [1,2,3,4,5] => 1

[1,2,3,5,4] => [1,2,3,4,5] => 1

[1,2,4,3,5] => [1,2,3,4,5] => 1

[1,2,4,5,3] => [1,2,3,4,5] => 1

[1,2,5,3,4] => [1,2,3,5,4] => 1

[1,2,5,4,3] => [1,2,3,5,4] => 1

[1,3,2,4,5] => [1,2,3,4,5] => 1

[1,3,2,5,4] => [1,2,3,4,5] => 1

[1,3,4,2,5] => [1,2,3,4,5] => 1

[1,3,4,5,2] => [1,2,3,4,5] => 1

[1,3,5,2,4] => [1,2,3,5,4] => 1

[1,3,5,4,2] => [1,2,3,5,4] => 1

[1,4,2,3,5] => [1,2,4,3,5] => 1

[1,4,2,5,3] => [1,2,4,5,3] => 1

[1,4,3,2,5] => [1,2,4,3,5] => 1

[1,4,3,5,2] => [1,2,4,5,3] => 1

[1,4,5,2,3] => [1,2,4,3,5] => 1

[1,4,5,3,2] => [1,2,4,3,5] => 1

[1,5,2,3,4] => [1,2,5,4,3] => 2

[1,5,2,4,3] => [1,2,5,3,4] => 1

[1,5,3,2,4] => [1,2,5,4,3] => 2

[1,5,3,4,2] => [1,2,5,3,4] => 1

[1,5,4,2,3] => [1,2,5,3,4] => 1

[1,5,4,3,2] => [1,2,5,3,4] => 1

[2,1,3,4,5] => [1,2,3,4,5] => 1

[2,1,3,5,4] => [1,2,3,4,5] => 1

[2,1,4,3,5] => [1,2,3,4,5] => 1

[2,1,4,5,3] => [1,2,3,4,5] => 1

[2,1,5,3,4] => [1,2,3,5,4] => 1

[2,1,5,4,3] => [1,2,3,5,4] => 1

[2,3,1,4,5] => [1,2,3,4,5] => 1

[2,3,1,5,4] => [1,2,3,4,5] => 1

[2,3,4,1,5] => [1,2,3,4,5] => 1

[2,3,4,5,1] => [1,2,3,4,5] => 1

[2,3,5,1,4] => [1,2,3,5,4] => 1

[2,3,5,4,1] => [1,2,3,5,4] => 1

[2,4,1,3,5] => [1,2,4,3,5] => 1

[2,4,1,5,3] => [1,2,4,5,3] => 1

[2,4,3,1,5] => [1,2,4,3,5] => 1

[2,4,3,5,1] => [1,2,4,5,3] => 1

[2,4,5,1,3] => [1,2,4,3,5] => 1

[2,4,5,3,1] => [1,2,4,3,5] => 1

[2,5,1,3,4] => [1,2,5,4,3] => 2

[2,5,1,4,3] => [1,2,5,3,4] => 1

[2,5,3,1,4] => [1,2,5,4,3] => 2

[2,5,3,4,1] => [1,2,5,3,4] => 1

[2,5,4,1,3] => [1,2,5,3,4] => 1

[2,5,4,3,1] => [1,2,5,3,4] => 1

[3,1,2,4,5] => [1,3,2,4,5] => 1

[3,1,2,5,4] => [1,3,2,4,5] => 1

[3,1,4,2,5] => [1,3,4,2,5] => 1

[3,1,4,5,2] => [1,3,4,5,2] => 1

[3,1,5,2,4] => [1,3,5,4,2] => 3

[3,1,5,4,2] => [1,3,5,2,4] => 2

[3,2,1,4,5] => [1,3,2,4,5] => 1

[3,2,1,5,4] => [1,3,2,4,5] => 1

[3,2,4,1,5] => [1,3,4,2,5] => 1

[3,2,4,5,1] => [1,3,4,5,2] => 1

[3,2,5,1,4] => [1,3,5,4,2] => 3

[3,2,5,4,1] => [1,3,5,2,4] => 2

[3,4,1,2,5] => [1,3,2,4,5] => 1

[3,4,1,5,2] => [1,3,2,4,5] => 1

[3,4,2,1,5] => [1,3,2,4,5] => 1

[3,4,2,5,1] => [1,3,2,4,5] => 1

[3,4,5,1,2] => [1,3,5,2,4] => 2

[3,4,5,2,1] => [1,3,5,2,4] => 2

[3,5,1,2,4] => [1,3,2,5,4] => 2

[3,5,1,4,2] => [1,3,2,5,4] => 2

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Description

The number of reduced words for a permutation.
This is the number of ways to write a permutation as a minimal length product of simple transpositions. E.g., there are two reduced words for the permutation $[3,2,1]$, which are $(1,2)(2,3)(1,2) = (2,3)(1,2)(2,3)$.

Map

cycle-as-one-line notation

Description

Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.