Identifier
-
Mp00223:
Permutations
—runsort⟶
Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001896: Signed permutations ⟶ ℤ
Values
[1] => [1] => [1] => [1] => 0
[1,2] => [1,2] => [1,2] => [1,2] => 0
[2,1] => [1,2] => [1,2] => [1,2] => 0
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 1
[2,1,3] => [1,3,2] => [3,1,2] => [3,1,2] => 1
[2,3,1] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[3,1,2] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[3,2,1] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [4,1,2,3] => [4,1,2,3] => 1
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,3,4,2] => [1,3,4,2] => [3,1,2,4] => [3,1,2,4] => 1
[1,4,2,3] => [1,4,2,3] => [1,4,2,3] => [1,4,2,3] => 1
[1,4,3,2] => [1,4,2,3] => [1,4,2,3] => [1,4,2,3] => 1
[2,1,3,4] => [1,3,4,2] => [3,1,2,4] => [3,1,2,4] => 1
[2,1,4,3] => [1,4,2,3] => [1,4,2,3] => [1,4,2,3] => 1
[2,3,1,4] => [1,4,2,3] => [1,4,2,3] => [1,4,2,3] => 1
[2,3,4,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[2,4,1,3] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[2,4,3,1] => [1,2,4,3] => [4,1,2,3] => [4,1,2,3] => 1
[3,1,2,4] => [1,2,4,3] => [4,1,2,3] => [4,1,2,3] => 1
[3,1,4,2] => [1,4,2,3] => [1,4,2,3] => [1,4,2,3] => 1
[3,2,1,4] => [1,4,2,3] => [1,4,2,3] => [1,4,2,3] => 1
[3,2,4,1] => [1,2,4,3] => [4,1,2,3] => [4,1,2,3] => 1
[3,4,1,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[3,4,2,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,1,2,3] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,1,3,2] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[4,2,1,3] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[4,2,3,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,3,1,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,4,3,5] => [1,2,4,3,5] => [1,4,2,3,5] => [1,4,2,3,5] => 1
[1,2,5,3,4] => [1,2,5,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => 1
[1,2,5,4,3] => [1,2,5,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => 1
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,4,2,5] => [1,3,4,2,5] => 1
[1,3,4,2,5] => [1,3,4,2,5] => [1,3,2,4,5] => [1,3,2,4,5] => 1
[1,4,2,3,5] => [1,4,2,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[1,4,3,5,2] => [1,4,2,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[1,5,2,3,4] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[1,5,3,4,2] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[1,5,4,2,3] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[1,5,4,3,2] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[2,1,4,3,5] => [1,4,2,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[2,1,5,3,4] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[2,1,5,4,3] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[2,3,1,5,4] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[2,3,4,1,5] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[2,3,5,1,4] => [1,4,2,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[2,4,3,5,1] => [1,2,4,3,5] => [1,4,2,3,5] => [1,4,2,3,5] => 1
[2,4,5,1,3] => [1,3,2,4,5] => [1,3,4,2,5] => [1,3,4,2,5] => 1
[2,5,1,3,4] => [1,3,4,2,5] => [1,3,2,4,5] => [1,3,2,4,5] => 1
[2,5,3,4,1] => [1,2,5,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => 1
[2,5,4,3,1] => [1,2,5,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => 1
[3,1,2,5,4] => [1,2,5,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => 1
[3,1,5,4,2] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[3,2,1,5,4] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[3,2,5,4,1] => [1,2,5,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => 1
[3,4,1,2,5] => [1,2,5,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => 1
[3,4,1,5,2] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[3,4,2,1,5] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[3,4,2,5,1] => [1,2,5,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => 1
[3,4,5,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[3,4,5,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[3,5,1,2,4] => [1,2,4,3,5] => [1,4,2,3,5] => [1,4,2,3,5] => 1
[3,5,1,4,2] => [1,4,2,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[3,5,2,1,4] => [1,4,2,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[3,5,2,4,1] => [1,2,4,3,5] => [1,4,2,3,5] => [1,4,2,3,5] => 1
[4,1,2,5,3] => [1,2,5,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => 1
[4,1,5,2,3] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[4,1,5,3,2] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[4,2,1,5,3] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[4,2,3,1,5] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[4,2,5,3,1] => [1,2,5,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => 1
[4,3,1,2,5] => [1,2,5,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => 1
[4,3,1,5,2] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[4,3,2,1,5] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[4,3,2,5,1] => [1,2,5,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => 1
[4,5,1,2,3] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,5,1,3,2] => [1,3,2,4,5] => [1,3,4,2,5] => [1,3,4,2,5] => 1
[4,5,2,1,3] => [1,3,2,4,5] => [1,3,4,2,5] => [1,3,4,2,5] => 1
[4,5,2,3,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,5,3,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,5,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,1,2,3,4] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,1,2,4,3] => [1,2,4,3,5] => [1,4,2,3,5] => [1,4,2,3,5] => 1
[5,1,3,2,4] => [1,3,2,4,5] => [1,3,4,2,5] => [1,3,4,2,5] => 1
[5,1,3,4,2] => [1,3,4,2,5] => [1,3,2,4,5] => [1,3,2,4,5] => 1
[5,1,4,2,3] => [1,4,2,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[5,1,4,3,2] => [1,4,2,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[5,2,1,3,4] => [1,3,4,2,5] => [1,3,2,4,5] => [1,3,2,4,5] => 1
[5,2,1,4,3] => [1,4,2,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[5,2,3,1,4] => [1,4,2,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[5,2,3,4,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,2,4,1,3] => [1,3,2,4,5] => [1,3,4,2,5] => [1,3,4,2,5] => 1
[5,2,4,3,1] => [1,2,4,3,5] => [1,4,2,3,5] => [1,4,2,3,5] => 1
[5,3,1,2,4] => [1,2,4,3,5] => [1,4,2,3,5] => [1,4,2,3,5] => 1
[5,3,1,4,2] => [1,4,2,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
>>> Load all 111 entries. <<<
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searching the database for statistics with the same generating function
Description
The number of right descents of a signed permutations.
An index is a right descent if it is a left descent of the inverse signed permutation.
An index is a right descent if it is a left descent of the inverse signed permutation.
Map
cactus evacuation
Description
The cactus evacuation of a permutation.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
Map
to signed permutation
Description
The signed permutation with all signs positive.
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