- FindStat

Identifier

Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St000530: Permutations ⟶ ℤ

Values

[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] => 2

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

[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] => 3

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

[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] => 3

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => 4

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

[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] => 4

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

[1,4,2,3,5] => [1,2,4,3,5] => 9

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

[1,4,3,2,5] => [1,2,4,3,5] => 9

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

[1,4,5,2,3] => [1,2,4,3,5] => 9

[1,4,5,3,2] => [1,2,4,3,5] => 9

[1,5,2,3,4] => [1,2,5,4,3] => 6

[1,5,2,4,3] => [1,2,5,3,4] => 9

[1,5,3,2,4] => [1,2,5,4,3] => 6

[1,5,3,4,2] => [1,2,5,3,4] => 9

[1,5,4,2,3] => [1,2,5,3,4] => 9

[1,5,4,3,2] => [1,2,5,3,4] => 9

[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] => 4

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

[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] => 4

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

[2,4,1,3,5] => [1,2,4,3,5] => 9

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

[2,4,3,1,5] => [1,2,4,3,5] => 9

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

[2,4,5,1,3] => [1,2,4,3,5] => 9

[2,4,5,3,1] => [1,2,4,3,5] => 9

[2,5,1,3,4] => [1,2,5,4,3] => 6

[2,5,1,4,3] => [1,2,5,3,4] => 9

[2,5,3,1,4] => [1,2,5,4,3] => 6

[2,5,3,4,1] => [1,2,5,3,4] => 9

[2,5,4,1,3] => [1,2,5,3,4] => 9

[2,5,4,3,1] => [1,2,5,3,4] => 9

[3,1,2,4,5] => [1,3,2,4,5] => 9

[3,1,2,5,4] => [1,3,2,4,5] => 9

[3,1,4,2,5] => [1,3,4,2,5] => 9

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

[3,1,5,2,4] => [1,3,5,4,2] => 6

[3,1,5,4,2] => [1,3,5,2,4] => 9

[3,2,1,4,5] => [1,3,2,4,5] => 9

[3,2,1,5,4] => [1,3,2,4,5] => 9

[3,2,4,1,5] => [1,3,4,2,5] => 9

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

[3,2,5,1,4] => [1,3,5,4,2] => 6

[3,2,5,4,1] => [1,3,5,2,4] => 9

[3,4,1,2,5] => [1,3,2,4,5] => 9

[3,4,1,5,2] => [1,3,2,4,5] => 9

[3,4,2,1,5] => [1,3,2,4,5] => 9

[3,4,2,5,1] => [1,3,2,4,5] => 9

[3,4,5,1,2] => [1,3,5,2,4] => 9

[3,4,5,2,1] => [1,3,5,2,4] => 9

[3,5,1,2,4] => [1,3,2,5,4] => 16

[3,5,1,4,2] => [1,3,2,5,4] => 16

[3,5,2,1,4] => [1,3,2,5,4] => 16

>>> Load all 3602 entries. <<<

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Description

The number of permutations with the same descent word as the given permutation.
The descent word of a permutation is the binary word given by Mp00109descent word. For a given permutation, this statistic is the number of permutations with the same descent word, so the number of elements in the fiber of the map Mp00109descent word containing a given permutation.
This statistic appears as up-down analysis in statistical applications in genetics, see [1] and the references therein.

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.