- FindStat

Identifier

Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St000756: Permutations ⟶ ℤ

Values

[1] => [1] => 1

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

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

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

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

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

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

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

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

[1,2,3,4] => [1,2,3,4] => 10

[1,2,4,3] => [1,2,3,4] => 10

[1,3,2,4] => [1,2,3,4] => 10

[1,3,4,2] => [1,2,3,4] => 10

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

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

[2,1,3,4] => [1,2,3,4] => 10

[2,1,4,3] => [1,2,3,4] => 10

[2,3,1,4] => [1,2,3,4] => 10

[2,3,4,1] => [1,2,3,4] => 10

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

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

[3,1,2,4] => [1,3,2,4] => 7

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

[3,2,1,4] => [1,3,2,4] => 7

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

[3,4,1,2] => [1,3,2,4] => 7

[3,4,2,1] => [1,3,2,4] => 7

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

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

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

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

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

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

[1,2,3,4,5] => [1,2,3,4,5] => 15

[1,2,3,5,4] => [1,2,3,4,5] => 15

[1,2,4,3,5] => [1,2,3,4,5] => 15

[1,2,4,5,3] => [1,2,3,4,5] => 15

[1,2,5,3,4] => [1,2,3,5,4] => 10

[1,2,5,4,3] => [1,2,3,5,4] => 10

[1,3,2,4,5] => [1,2,3,4,5] => 15

[1,3,2,5,4] => [1,2,3,4,5] => 15

[1,3,4,2,5] => [1,2,3,4,5] => 15

[1,3,4,5,2] => [1,2,3,4,5] => 15

[1,3,5,2,4] => [1,2,3,5,4] => 10

[1,3,5,4,2] => [1,2,3,5,4] => 10

[1,4,2,3,5] => [1,2,4,3,5] => 11

[1,4,2,5,3] => [1,2,4,5,3] => 10

[1,4,3,2,5] => [1,2,4,3,5] => 11

[1,4,3,5,2] => [1,2,4,5,3] => 10

[1,4,5,2,3] => [1,2,4,3,5] => 11

[1,4,5,3,2] => [1,2,4,3,5] => 11

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

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

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

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

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

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

[2,1,3,4,5] => [1,2,3,4,5] => 15

[2,1,3,5,4] => [1,2,3,4,5] => 15

[2,1,4,3,5] => [1,2,3,4,5] => 15

[2,1,4,5,3] => [1,2,3,4,5] => 15

[2,1,5,3,4] => [1,2,3,5,4] => 10

[2,1,5,4,3] => [1,2,3,5,4] => 10

[2,3,1,4,5] => [1,2,3,4,5] => 15

[2,3,1,5,4] => [1,2,3,4,5] => 15

[2,3,4,1,5] => [1,2,3,4,5] => 15

[2,3,4,5,1] => [1,2,3,4,5] => 15

[2,3,5,1,4] => [1,2,3,5,4] => 10

[2,3,5,4,1] => [1,2,3,5,4] => 10

[2,4,1,3,5] => [1,2,4,3,5] => 11

[2,4,1,5,3] => [1,2,4,5,3] => 10

[2,4,3,1,5] => [1,2,4,3,5] => 11

[2,4,3,5,1] => [1,2,4,5,3] => 10

[2,4,5,1,3] => [1,2,4,3,5] => 11

[2,4,5,3,1] => [1,2,4,3,5] => 11

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

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

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

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

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

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

[3,1,2,4,5] => [1,3,2,4,5] => 12

[3,1,2,5,4] => [1,3,2,4,5] => 12

[3,1,4,2,5] => [1,3,4,2,5] => 11

[3,1,4,5,2] => [1,3,4,5,2] => 10

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

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

[3,2,1,4,5] => [1,3,2,4,5] => 12

[3,2,1,5,4] => [1,3,2,4,5] => 12

[3,2,4,1,5] => [1,3,4,2,5] => 11

[3,2,4,5,1] => [1,3,4,5,2] => 10

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

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

[3,4,1,2,5] => [1,3,2,4,5] => 12

[3,4,1,5,2] => [1,3,2,4,5] => 12

[3,4,2,1,5] => [1,3,2,4,5] => 12

[3,4,2,5,1] => [1,3,2,4,5] => 12

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

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

[3,5,1,2,4] => [1,3,2,5,4] => 7

[3,5,1,4,2] => [1,3,2,5,4] => 7

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Description

The sum of the positions of the left to right maxima of a permutation.
The generating function for this statistic is $$\sum_{\pi\in\mathfrak S_n} q^{slrmax(pi)} = \prod_{k=1}^n (q^k+k-1),$$
see [prop. 2.6., 1].

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.