Identifier
Values
[1] => [1,0] => 1
[1,1] => [1,0,1,0] => 1
[2] => [1,1,0,0] => 1
[1,1,1] => [1,0,1,0,1,0] => 1
[1,2] => [1,0,1,1,0,0] => 1
[2,1] => [1,1,0,0,1,0] => 1
[3] => [1,1,1,0,0,0] => 2
[1,1,1,1] => [1,0,1,0,1,0,1,0] => 1
[1,1,2] => [1,0,1,0,1,1,0,0] => 1
[1,2,1] => [1,0,1,1,0,0,1,0] => 1
[1,3] => [1,0,1,1,1,0,0,0] => 2
[2,1,1] => [1,1,0,0,1,0,1,0] => 1
[2,2] => [1,1,0,0,1,1,0,0] => 1
[3,1] => [1,1,1,0,0,0,1,0] => 2
[4] => [1,1,1,1,0,0,0,0] => 7
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,4] => [1,0,1,1,1,1,0,0,0,0] => 7
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
[2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[4,1] => [1,1,1,1,0,0,0,0,1,0] => 7
[5] => [1,1,1,1,1,0,0,0,0,0] => 42
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 7
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 42
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 7
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 4
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 7
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 7
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 42
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 429
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Description
The number of alternating sign matrices for a given Dyck path.
The Dyck path is given by the last diagonal of the monotone triangle corresponding to an alternating sign matrix.
Map
bounce path
Description
The bounce path determined by an integer composition.