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*       www.FindStat.org - The Combinatorial Statistic Finder               *
*                                                                           *
*       Copyright (C) 2019 The FindStatCrew <info@findstat.org>             *
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*    This information is distributed in the hope that it will be useful,    *
*    but WITHOUT ANY WARRANTY; without even the implied warranty of         *
*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.                   *
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-----------------------------------------------------------------------------
Statistic identifier: St000331

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

-----------------------------------------------------------------------------
Description: The number of upper interactions of a Dyck path.

An ''upper interaction'' in a Dyck path is defined as the occurrence of a factor '''$A^{k}$$B^{k}$''' for any '''${k ≥ 1}$''', where '''${A}$''' is a down-step and '''${B}$''' is a up-step. 

-----------------------------------------------------------------------------
References: [1]   [[http://www.emis.de/journals/SLC/wpapers/s54leborgne.pdf]]

-----------------------------------------------------------------------------
Code:
def statistic(List):
    interactions = 0
    i = 0
    count = 0
    while i < len(List):
        if List[i] == 0:
            if List[i-1] == 1:
                count = 0
            count = count + 1
        if List[i] == 1 and count > 0:
            interactions = interactions + 1
            count = count - 1
        i  = i + 1
    return interactions

-----------------------------------------------------------------------------
Statistic values:

[1,0]                     => 0
[1,0,1,0]                 => 1
[1,1,0,0]                 => 0
[1,0,1,0,1,0]             => 2
[1,0,1,1,0,0]             => 1
[1,1,0,0,1,0]             => 1
[1,1,0,1,0,0]             => 1
[1,1,1,0,0,0]             => 0
[1,0,1,0,1,0,1,0]         => 3
[1,0,1,0,1,1,0,0]         => 2
[1,0,1,1,0,0,1,0]         => 2
[1,0,1,1,0,1,0,0]         => 2
[1,0,1,1,1,0,0,0]         => 1
[1,1,0,0,1,0,1,0]         => 2
[1,1,0,0,1,1,0,0]         => 2
[1,1,0,1,0,0,1,0]         => 2
[1,1,0,1,0,1,0,0]         => 2
[1,1,0,1,1,0,0,0]         => 1
[1,1,1,0,0,0,1,0]         => 1
[1,1,1,0,0,1,0,0]         => 1
[1,1,1,0,1,0,0,0]         => 1
[1,1,1,1,0,0,0,0]         => 0
[1,0,1,0,1,0,1,0,1,0]     => 4
[1,0,1,0,1,0,1,1,0,0]     => 3
[1,0,1,0,1,1,0,0,1,0]     => 3
[1,0,1,0,1,1,0,1,0,0]     => 3
[1,0,1,0,1,1,1,0,0,0]     => 2
[1,0,1,1,0,0,1,0,1,0]     => 3
[1,0,1,1,0,0,1,1,0,0]     => 3
[1,0,1,1,0,1,0,0,1,0]     => 3
[1,0,1,1,0,1,0,1,0,0]     => 3
[1,0,1,1,0,1,1,0,0,0]     => 2
[1,0,1,1,1,0,0,0,1,0]     => 2
[1,0,1,1,1,0,0,1,0,0]     => 2
[1,0,1,1,1,0,1,0,0,0]     => 2
[1,0,1,1,1,1,0,0,0,0]     => 1
[1,1,0,0,1,0,1,0,1,0]     => 3
[1,1,0,0,1,0,1,1,0,0]     => 2
[1,1,0,0,1,1,0,0,1,0]     => 3
[1,1,0,0,1,1,0,1,0,0]     => 3
[1,1,0,0,1,1,1,0,0,0]     => 2
[1,1,0,1,0,0,1,0,1,0]     => 3
[1,1,0,1,0,0,1,1,0,0]     => 3
[1,1,0,1,0,1,0,0,1,0]     => 3
[1,1,0,1,0,1,0,1,0,0]     => 3
[1,1,0,1,0,1,1,0,0,0]     => 2
[1,1,0,1,1,0,0,0,1,0]     => 2
[1,1,0,1,1,0,0,1,0,0]     => 2
[1,1,0,1,1,0,1,0,0,0]     => 2
[1,1,0,1,1,1,0,0,0,0]     => 1
[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]     => 2
[1,1,1,0,0,1,0,1,0,0]     => 2
[1,1,1,0,0,1,1,0,0,0]     => 2
[1,1,1,0,1,0,0,0,1,0]     => 2
[1,1,1,0,1,0,0,1,0,0]     => 2
[1,1,1,0,1,0,1,0,0,0]     => 2
[1,1,1,0,1,1,0,0,0,0]     => 1
[1,1,1,1,0,0,0,0,1,0]     => 1
[1,1,1,1,0,0,0,1,0,0]     => 1
[1,1,1,1,0,0,1,0,0,0]     => 1
[1,1,1,1,0,1,0,0,0,0]     => 1
[1,1,1,1,1,0,0,0,0,0]     => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => 3
[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] => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => 4
[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] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => 3
[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] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => 0

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Created: Dec 17, 2015 at 23:15 by Mike Gaudette

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Last Updated: May 20, 2016 at 20:54 by Martin Rubey