Identifier
- St000079: Dyck paths ⟶ ℤ
Values
[1,0] => 1
[1,0,1,0] => 1
[1,1,0,0] => 1
[1,0,1,0,1,0] => 1
[1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => 1
[1,1,0,1,0,0] => 2
[1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,0,0] => 5
[1,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,0] => 5
[1,1,1,0,1,0,0,0] => 7
[1,1,1,1,0,0,0,0] => 7
[1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0] => 14
[1,1,0,1,0,1,1,0,0,0] => 14
[1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,0] => 14
[1,1,0,1,1,0,1,0,0,0] => 21
[1,1,0,1,1,1,0,0,0,0] => 21
[1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,0] => 14
[1,1,1,0,0,1,1,0,0,0] => 14
[1,1,1,0,1,0,0,0,1,0] => 7
[1,1,1,0,1,0,0,1,0,0] => 21
[1,1,1,0,1,0,1,0,0,0] => 35
[1,1,1,0,1,1,0,0,0,0] => 35
[1,1,1,1,0,0,0,0,1,0] => 7
[1,1,1,1,0,0,0,1,0,0] => 21
[1,1,1,1,0,0,1,0,0,0] => 35
[1,1,1,1,0,1,0,0,0,0] => 42
[1,1,1,1,1,0,0,0,0,0] => 42
[1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,1,0,0,0] => 7
[1,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,0] => 14
[1,0,1,1,0,1,0,1,1,0,0,0] => 14
[1,0,1,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,0] => 14
[1,0,1,1,0,1,1,0,1,0,0,0] => 21
[1,0,1,1,0,1,1,1,0,0,0,0] => 21
[1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,0] => 14
[1,0,1,1,1,0,0,1,1,0,0,0] => 14
[1,0,1,1,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,0,1,0,0] => 21
[1,0,1,1,1,0,1,0,1,0,0,0] => 35
[1,0,1,1,1,0,1,1,0,0,0,0] => 35
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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.
The Dyck path is given by the last diagonal of the monotone triangle corresponding to an alternating sign matrix.
Code
def statistic(self):
return sum( 1 for a in AlternatingSignMatrices(len(list(self))/2) if a.to_dyck_word(algorithm = 'last_diagonal') == self )
Created
Jun 11, 2013 at 21:17 by Jessica Striker
Updated
Aug 21, 2017 at 08:49 by Martin Rubey
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