Identifier
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. <<<
[5,3,2,1,4] => [1,4,2,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[5,3,2,4,1] => [1,2,4,3,5] => [1,4,2,3,5] => [1,4,2,3,5] => 1
[5,3,4,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,3,4,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,1,2,3] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,1,3,2] => [1,3,2,4,5] => [1,3,4,2,5] => [1,3,4,2,5] => 1
[5,4,2,1,3] => [1,3,2,4,5] => [1,3,4,2,5] => [1,3,4,2,5] => 1
[5,4,2,3,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,3,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
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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.
Map
to signed permutation
Description
The signed permutation with all signs positive.
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.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.