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*       Copyright (C) 2019 The FindStatCrew <info@findstat.org>             *
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Statistic identifier: St000079

-----------------------------------------------------------------------------
Collection: Dyck paths

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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.

-----------------------------------------------------------------------------
References: 

-----------------------------------------------------------------------------
Code:
def statistic(self):
    return sum( 1 for a in AlternatingSignMatrices(len(list(self))/2) if a.to_dyck_word(algorithm = 'last_diagonal') == self )

-----------------------------------------------------------------------------
Statistic 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
[1,0,1,1,1,1,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,0,0,0,1,0,0] => 21
[1,0,1,1,1,1,0,0,1,0,0,0] => 35
[1,0,1,1,1,1,0,1,0,0,0,0] => 42
[1,0,1,1,1,1,1,0,0,0,0,0] => 42
[1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,0] => 14
[1,1,0,1,0,1,0,1,0,1,0,0] => 42
[1,1,0,1,0,1,0,1,1,0,0,0] => 42
[1,1,0,1,0,1,1,0,0,0,1,0] => 14
[1,1,0,1,0,1,1,0,0,1,0,0] => 42
[1,1,0,1,0,1,1,0,1,0,0,0] => 65
[1,1,0,1,0,1,1,1,0,0,0,0] => 65
[1,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,0] => 14
[1,1,0,1,1,0,0,1,0,1,0,0] => 42
[1,1,0,1,1,0,0,1,1,0,0,0] => 42
[1,1,0,1,1,0,1,0,0,0,1,0] => 21
[1,1,0,1,1,0,1,0,0,1,0,0] => 68
[1,1,0,1,1,0,1,0,1,0,0,0] => 119
[1,1,0,1,1,0,1,1,0,0,0,0] => 119
[1,1,0,1,1,1,0,0,0,0,1,0] => 21
[1,1,0,1,1,1,0,0,0,1,0,0] => 68
[1,1,0,1,1,1,0,0,1,0,0,0] => 119
[1,1,0,1,1,1,0,1,0,0,0,0] => 147
[1,1,0,1,1,1,1,0,0,0,0,0] => 147
[1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,1,1,0,0,1,0,1,0,0,1,0] => 14
[1,1,1,0,0,1,0,1,0,1,0,0] => 42
[1,1,1,0,0,1,0,1,1,0,0,0] => 42
[1,1,1,0,0,1,1,0,0,0,1,0] => 14
[1,1,1,0,0,1,1,0,0,1,0,0] => 42
[1,1,1,0,0,1,1,0,1,0,0,0] => 65
[1,1,1,0,0,1,1,1,0,0,0,0] => 65
[1,1,1,0,1,0,0,0,1,0,1,0] => 7
[1,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,1,1,0,1,0,0,1,0,0,1,0] => 21
[1,1,1,0,1,0,0,1,0,1,0,0] => 65
[1,1,1,0,1,0,0,1,1,0,0,0] => 65
[1,1,1,0,1,0,1,0,0,0,1,0] => 35
[1,1,1,0,1,0,1,0,0,1,0,0] => 119
[1,1,1,0,1,0,1,0,1,0,0,0] => 219
[1,1,1,0,1,0,1,1,0,0,0,0] => 219
[1,1,1,0,1,1,0,0,0,0,1,0] => 35
[1,1,1,0,1,1,0,0,0,1,0,0] => 119
[1,1,1,0,1,1,0,0,1,0,0,0] => 219
[1,1,1,0,1,1,0,1,0,0,0,0] => 282
[1,1,1,0,1,1,1,0,0,0,0,0] => 282
[1,1,1,1,0,0,0,0,1,0,1,0] => 7
[1,1,1,1,0,0,0,0,1,1,0,0] => 7
[1,1,1,1,0,0,0,1,0,0,1,0] => 21
[1,1,1,1,0,0,0,1,0,1,0,0] => 65
[1,1,1,1,0,0,0,1,1,0,0,0] => 65
[1,1,1,1,0,0,1,0,0,0,1,0] => 35
[1,1,1,1,0,0,1,0,0,1,0,0] => 119
[1,1,1,1,0,0,1,0,1,0,0,0] => 219
[1,1,1,1,0,0,1,1,0,0,0,0] => 219
[1,1,1,1,0,1,0,0,0,0,1,0] => 42
[1,1,1,1,0,1,0,0,0,1,0,0] => 147
[1,1,1,1,0,1,0,0,1,0,0,0] => 282
[1,1,1,1,0,1,0,1,0,0,0,0] => 387
[1,1,1,1,0,1,1,0,0,0,0,0] => 387
[1,1,1,1,1,0,0,0,0,0,1,0] => 42
[1,1,1,1,1,0,0,0,0,1,0,0] => 147
[1,1,1,1,1,0,0,0,1,0,0,0] => 282
[1,1,1,1,1,0,0,1,0,0,0,0] => 387
[1,1,1,1,1,0,1,0,0,0,0,0] => 429
[1,1,1,1,1,1,0,0,0,0,0,0] => 429

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Created: Jun 11, 2013 at 21:17 by Jessica Striker

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Last Updated: Aug 21, 2017 at 08:49 by Martin Rubey