Identifier
Values
[1,0] => [1] => [1] => [1] => 1
[1,0,1,0] => [2,1] => [2,1] => [2,1] => 1
[1,1,0,0] => [1,2] => [1,2] => [1,2] => 2
[1,0,1,0,1,0] => [3,2,1] => [3,2,1] => [3,2,1] => 2
[1,0,1,1,0,0] => [2,3,1] => [3,1,2] => [3,1,2] => 1
[1,1,0,0,1,0] => [3,1,2] => [1,3,2] => [1,3,2] => 2
[1,1,0,1,0,0] => [2,1,3] => [2,1,3] => [2,1,3] => 2
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [1,2,3] => 3
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 2
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [4,3,1,2] => [4,3,1,2] => 2
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 2
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [4,2,1,3] => [4,2,1,3] => 2
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [4,1,2,3] => [4,1,2,3] => 1
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [1,4,3,2] => [1,4,3,2] => 3
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [1,4,2,3] => [1,4,2,3] => 2
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [3,1,4,2] => [3,1,4,2] => 2
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 3
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [3,1,2,4] => [3,1,2,4] => 2
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [1,2,4,3] => [1,2,4,3] => 3
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [1,3,2,4] => [1,3,2,4] => 3
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 3
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [1,5,4,2,3] => [1,5,4,2,3] => 3
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [1,5,2,4,3] => [1,5,2,4,3] => 3
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [1,5,3,2,4] => [1,5,3,2,4] => 3
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [1,5,2,3,4] => [1,5,2,3,4] => 2
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [1,2,5,4,3] => [1,2,5,4,3] => 4
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [1,2,5,3,4] => [1,2,5,3,4] => 3
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [1,4,2,5,3] => [1,4,2,5,3] => 3
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 4
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [1,4,2,3,5] => [1,4,2,3,5] => 3
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [1,2,3,5,4] => [1,2,3,5,4] => 4
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 4
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 4
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 5
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Description
The number of weak excedances of a signed permutation.
For a signed permutation $\pi\in\mathfrak H_n$, this is $\lvert\{i\in[n] \mid \pi(i) \geq i\}\rvert$.
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].