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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: St001567

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Collection: Decorated permutations

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Description: The number of weak exceedances of a decorated permutation.

A '''weak exceedance''' of a decorated permutation $\tau$ is a position $i$ such that $i > \tau(i)$ or $i = \tau(i)$ and $\tau(i)$ has positive decoration.

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References: 

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Code:


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Statistic values:

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

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Created: Jul 15, 2020 at 15:35 by Dylan Heuer

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Last Updated: Jul 15, 2020 at 15:35 by Dylan Heuer