Identifier
Values
[1,0] => [1] => [1] => 1
[1,0,1,0] => [2,1] => [2,1] => 1
[1,1,0,0] => [1,2] => [1,2] => 1
[1,0,1,0,1,0] => [3,2,1] => [3,2,1] => 2
[1,0,1,1,0,0] => [2,3,1] => [2,3,1] => 1
[1,1,0,0,1,0] => [3,1,2] => [3,1,2] => 1
[1,1,0,1,0,0] => [2,1,3] => [2,1,3] => 1
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => 1
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [4,3,2,1] => 16
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [3,4,2,1] => 5
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [4,2,3,1] => 6
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [3,2,4,1] => 3
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [2,3,4,1] => 1
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [4,3,1,2] => 5
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [3,4,1,2] => 2
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [4,2,1,3] => 3
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [3,2,1,4] => 2
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [2,3,1,4] => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [4,1,2,3] => 1
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [3,1,2,4] => 1
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => 1
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Description
The number of reduced words of a signed permutation.
This is the number of ways to write a permutation as a minimal length product of simple reflections.
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].