Identifier
Values
[1,0] => [1] => 1
[1,0,1,0] => [2,1] => 1
[1,1,0,0] => [1,2] => 2
[1,0,1,0,1,0] => [3,2,1] => 1
[1,0,1,1,0,0] => [2,3,1] => 2
[1,1,0,0,1,0] => [3,1,2] => 2
[1,1,0,1,0,0] => [2,1,3] => 4
[1,1,1,0,0,0] => [1,2,3] => 6
[1,0,1,0,1,0,1,0] => [4,3,2,1] => 1
[1,0,1,0,1,1,0,0] => [3,4,2,1] => 2
[1,0,1,1,0,0,1,0] => [4,2,3,1] => 2
[1,0,1,1,0,1,0,0] => [3,2,4,1] => 4
[1,0,1,1,1,0,0,0] => [2,3,4,1] => 6
[1,1,0,0,1,0,1,0] => [4,3,1,2] => 2
[1,1,0,0,1,1,0,0] => [3,4,1,2] => 4
[1,1,0,1,0,0,1,0] => [4,2,1,3] => 4
[1,1,0,1,0,1,0,0] => [3,2,1,4] => 8
[1,1,0,1,1,0,0,0] => [2,3,1,4] => 12
[1,1,1,0,0,0,1,0] => [4,1,2,3] => 6
[1,1,1,0,0,1,0,0] => [3,1,2,4] => 12
[1,1,1,0,1,0,0,0] => [2,1,3,4] => 18
[1,1,1,1,0,0,0,0] => [1,2,3,4] => 24
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 1
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 2
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => 2
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => 4
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 6
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => 2
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 4
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => 4
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 8
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 12
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 6
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 12
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 18
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 24
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => 2
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 4
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 4
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 8
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 12
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => 4
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 8
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => 8
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => 16
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => 24
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 12
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => 24
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => 36
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => 48
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 6
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 12
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 12
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => 24
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => 36
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 18
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => 36
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => 54
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => 72
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 24
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => 48
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => 72
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => 96
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => 120
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Description
The number of permutations greater than or equal to the given permutation in (strong) Bruhat order.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].