- FindStat

Identifier

Mp00252: Permutations —restriction⟶ Permutations
St000099: Permutations ⟶ ℤ (values match St000023The number of inner peaks of a permutation.)

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 5912 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 valleys of a permutation, including the boundary.
The number of valleys excluding the boundary is St000353The number of inner valleys of a permutation..

Map

restriction

Description

The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.