- FindStat

Identifier

Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001855: Signed permutations ⟶ ℤ

Values

[1] => [1] => 1
[1,2] => [1,2] => 1
[2,1] => [2,1] => 2
[1,2,3] => [1,2,3] => 1
[1,3,2] => [1,3,2] => 2
[2,1,3] => [2,1,3] => 2
[2,3,1] => [2,3,1] => 3
[3,1,2] => [3,1,2] => 3
[3,2,1] => [3,2,1] => 6
[1,2,3,4] => [1,2,3,4] => 1
[1,2,4,3] => [1,2,4,3] => 2
[1,3,2,4] => [1,3,2,4] => 2
[1,3,4,2] => [1,3,4,2] => 3
[1,4,2,3] => [1,4,2,3] => 3
[1,4,3,2] => [1,4,3,2] => 6
[2,1,3,4] => [2,1,3,4] => 2
[2,1,4,3] => [2,1,4,3] => 4
[2,3,1,4] => [2,3,1,4] => 3
[2,3,4,1] => [2,3,4,1] => 4
[2,4,1,3] => [2,4,1,3] => 5
[2,4,3,1] => [2,4,3,1] => 8
[3,1,2,4] => [3,1,2,4] => 3
[3,1,4,2] => [3,1,4,2] => 5
[3,2,1,4] => [3,2,1,4] => 6
[3,2,4,1] => [3,2,4,1] => 8
[3,4,1,2] => [3,4,1,2] => 6
[3,4,2,1] => [3,4,2,1] => 12
[4,1,2,3] => [4,1,2,3] => 4
[4,1,3,2] => [4,1,3,2] => 8
[4,2,1,3] => [4,2,1,3] => 8
[4,2,3,1] => [4,2,3,1] => 12
[4,3,1,2] => [4,3,1,2] => 12
[4,3,2,1] => [4,3,2,1] => 24
[1,2,3,4,5] => [1,2,3,4,5] => 1
[1,2,3,5,4] => [1,2,3,5,4] => 2
[1,2,4,3,5] => [1,2,4,3,5] => 2
[1,2,4,5,3] => [1,2,4,5,3] => 3
[1,2,5,3,4] => [1,2,5,3,4] => 3
[1,2,5,4,3] => [1,2,5,4,3] => 6
[1,3,2,4,5] => [1,3,2,4,5] => 2
[1,3,2,5,4] => [1,3,2,5,4] => 4
[1,3,4,2,5] => [1,3,4,2,5] => 3
[1,3,4,5,2] => [1,3,4,5,2] => 4
[1,3,5,2,4] => [1,3,5,2,4] => 5
[1,3,5,4,2] => [1,3,5,4,2] => 8
[1,4,2,3,5] => [1,4,2,3,5] => 3
[1,4,2,5,3] => [1,4,2,5,3] => 5
[1,4,3,2,5] => [1,4,3,2,5] => 6
[1,4,3,5,2] => [1,4,3,5,2] => 8
[1,4,5,2,3] => [1,4,5,2,3] => 6
[1,4,5,3,2] => [1,4,5,3,2] => 12
[1,5,2,3,4] => [1,5,2,3,4] => 4
[1,5,2,4,3] => [1,5,2,4,3] => 8
[1,5,3,2,4] => [1,5,3,2,4] => 8
[1,5,3,4,2] => [1,5,3,4,2] => 12
[1,5,4,2,3] => [1,5,4,2,3] => 12
[1,5,4,3,2] => [1,5,4,3,2] => 24

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

$F_{1} = q$

$F_{2} = q + q^{2}$

$F_{3} = q + 2\ q^{2} + 2\ q^{3} + q^{6}$

$F_{4} = q + 3\ q^{2} + 4\ q^{3} + 3\ q^{4} + 2\ q^{5} + 3\ q^{6} + 4\ q^{8} + 3\ q^{12} + q^{24}$

Description

The number of signed permutations less than or equal to a signed permutation in left weak order.

Map

to signed permutation

Description

The signed permutation with all signs positive.