Identifier
- St000226: Permutations ⟶ ℤ
Values
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 3
[2,1,3] => 0
[2,3,1] => 3
[3,1,2] => 0
[3,2,1] => 0
[1,2,3,4] => 0
[1,2,4,3] => 3
[1,3,2,4] => 3
[1,3,4,2] => 3
[1,4,2,3] => 5
[1,4,3,2] => 4
[2,1,3,4] => 1
[2,1,4,3] => 4
[2,3,1,4] => 3
[2,3,4,1] => 4
[2,4,1,3] => 5
[2,4,3,1] => 3
[3,1,2,4] => 0
[3,1,4,2] => 5
[3,2,1,4] => 0
[3,2,4,1] => 5
[3,4,1,2] => 4
[3,4,2,1] => 3
[4,1,2,3] => 0
[4,1,3,2] => 3
[4,2,1,3] => 0
[4,2,3,1] => 3
[4,3,1,2] => 1
[4,3,2,1] => 0
[1,2,3,4,5] => 0
[1,2,3,5,4] => 3
[1,2,4,3,5] => 3
[1,2,4,5,3] => 3
[1,2,5,3,4] => 5
[1,2,5,4,3] => 4
[1,3,2,4,5] => 3
[1,3,2,5,4] => 4
[1,3,4,2,5] => 3
[1,3,4,5,2] => 4
[1,3,5,2,4] => 5
[1,3,5,4,2] => 3
[1,4,2,3,5] => 5
[1,4,2,5,3] => 5
[1,4,3,2,5] => 4
[1,4,3,5,2] => 5
[1,4,5,2,3] => 4
[1,4,5,3,2] => 3
[1,5,2,3,4] => 7
[1,5,2,4,3] => 7
[1,5,3,2,4] => 6
[1,5,3,4,2] => 6
[1,5,4,2,3] => 5
[1,5,4,3,2] => 5
[2,1,3,4,5] => 1
[2,1,3,5,4] => 3
[2,1,4,3,5] => 4
[2,1,4,5,3] => 3
[2,1,5,3,4] => 6
[2,1,5,4,3] => 5
[2,3,1,4,5] => 3
[2,3,1,5,4] => 5
[2,3,4,1,5] => 4
[2,3,4,5,1] => 5
[2,3,5,1,4] => 6
[2,3,5,4,1] => 3
[2,4,1,3,5] => 5
[2,4,1,5,3] => 6
[2,4,3,1,5] => 3
[2,4,3,5,1] => 6
[2,4,5,1,3] => 5
[2,4,5,3,1] => 3
[2,5,1,3,4] => 7
[2,5,1,4,3] => 7
[2,5,3,1,4] => 5
[2,5,3,4,1] => 5
[2,5,4,1,3] => 4
[2,5,4,3,1] => 4
[3,1,2,4,5] => 1
[3,1,2,5,4] => 4
[3,1,4,2,5] => 5
[3,1,4,5,2] => 4
[3,1,5,2,4] => 7
[3,1,5,4,2] => 5
[3,2,1,4,5] => 2
[3,2,1,5,4] => 5
[3,2,4,1,5] => 5
[3,2,4,5,1] => 5
[3,2,5,1,4] => 7
[3,2,5,4,1] => 4
[3,4,1,2,5] => 4
[3,4,1,5,2] => 7
[3,4,2,1,5] => 3
[3,4,2,5,1] => 7
[3,4,5,1,2] => 5
[3,4,5,2,1] => 4
[3,5,1,2,4] => 6
[3,5,1,4,2] => 6
[3,5,2,1,4] => 5
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Description
The convexity of a permutation.
It is given by the maximal value of $2x_i-x_{i-1}-x_{i+1}$ over all $i \in \{2,\ldots,n-1\}$.
It is given by the maximal value of $2x_i-x_{i-1}-x_{i+1}$ over all $i \in \{2,\ldots,n-1\}$.
References
[1] Coscia, C., DeWitt, J. Locally Convex Words and Permutations arXiv:1410.7818
Code
def statistic(x):
return max([0] +[2*x[i]-x[i-1]-x[i+1] for i in range(1, len(x)-1)])
Created
Oct 30, 2014 at 07:58 by Christian Stump
Updated
May 29, 2015 at 17:23 by Martin Rubey
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