- FindStat

Identifier

Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
St000110: Permutations ⟶ ℤ

Values

[1] => [1] => [1] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[3,1,2,4] => [1,3,2,4] => [2,4,3,1] => 8

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

[3,2,1,4] => [1,3,2,4] => [2,4,3,1] => 8

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

[3,4,1,2] => [1,3,2,4] => [2,4,3,1] => 8

[3,4,2,1] => [1,3,2,4] => [2,4,3,1] => 8

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[3,1,5,4,2] => [1,3,5,2,4] => [2,4,1,5,3] => 8

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

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

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

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

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

[3,2,5,4,1] => [1,3,5,2,4] => [2,4,1,5,3] => 8

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

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

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

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

[3,4,5,1,2] => [1,3,5,2,4] => [2,4,1,5,3] => 8

[3,4,5,2,1] => [1,3,5,2,4] => [2,4,1,5,3] => 8

[3,5,1,2,4] => [1,3,2,5,4] => [2,4,3,1,5] => 8

[3,5,1,4,2] => [1,3,2,5,4] => [2,4,3,1,5] => 8

>>> Load all 1449 entries. <<<

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

The number of permutations less than or equal to a permutation in left weak order.
This is the same as the number of permutations less than or equal to the given permutation in right weak order.

Map

Lehmer code rotation

Description

Sends a permutation $\pi$ to the unique permutation $\tau$ (of the same length) such that every entry in the Lehmer code of $\tau$ is cyclically one larger than the Lehmer code of $\pi$.

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.