Identifier
- St000360: Permutations ⟶ ℤ
Values
[1] => 0
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 0
[2,1,3] => 0
[2,3,1] => 0
[3,1,2] => 0
[3,2,1] => 1
[1,2,3,4] => 0
[1,2,4,3] => 0
[1,3,2,4] => 0
[1,3,4,2] => 0
[1,4,2,3] => 0
[1,4,3,2] => 1
[2,1,3,4] => 0
[2,1,4,3] => 0
[2,3,1,4] => 0
[2,3,4,1] => 0
[2,4,1,3] => 0
[2,4,3,1] => 1
[3,1,2,4] => 0
[3,1,4,2] => 0
[3,2,1,4] => 1
[3,2,4,1] => 1
[3,4,1,2] => 0
[3,4,2,1] => 1
[4,1,2,3] => 0
[4,1,3,2] => 0
[4,2,1,3] => 1
[4,2,3,1] => 1
[4,3,1,2] => 2
[4,3,2,1] => 3
[1,2,3,4,5] => 0
[1,2,3,5,4] => 0
[1,2,4,3,5] => 0
[1,2,4,5,3] => 0
[1,2,5,3,4] => 0
[1,2,5,4,3] => 1
[1,3,2,4,5] => 0
[1,3,2,5,4] => 0
[1,3,4,2,5] => 0
[1,3,4,5,2] => 0
[1,3,5,2,4] => 0
[1,3,5,4,2] => 1
[1,4,2,3,5] => 0
[1,4,2,5,3] => 0
[1,4,3,2,5] => 1
[1,4,3,5,2] => 1
[1,4,5,2,3] => 0
[1,4,5,3,2] => 1
[1,5,2,3,4] => 0
[1,5,2,4,3] => 0
[1,5,3,2,4] => 1
[1,5,3,4,2] => 1
[1,5,4,2,3] => 2
[1,5,4,3,2] => 3
[2,1,3,4,5] => 0
[2,1,3,5,4] => 0
[2,1,4,3,5] => 0
[2,1,4,5,3] => 0
[2,1,5,3,4] => 0
[2,1,5,4,3] => 1
[2,3,1,4,5] => 0
[2,3,1,5,4] => 0
[2,3,4,1,5] => 0
[2,3,4,5,1] => 0
[2,3,5,1,4] => 0
[2,3,5,4,1] => 1
[2,4,1,3,5] => 0
[2,4,1,5,3] => 0
[2,4,3,1,5] => 1
[2,4,3,5,1] => 1
[2,4,5,1,3] => 0
[2,4,5,3,1] => 1
[2,5,1,3,4] => 0
[2,5,1,4,3] => 0
[2,5,3,1,4] => 1
[2,5,3,4,1] => 1
[2,5,4,1,3] => 2
[2,5,4,3,1] => 3
[3,1,2,4,5] => 0
[3,1,2,5,4] => 0
[3,1,4,2,5] => 0
[3,1,4,5,2] => 0
[3,1,5,2,4] => 0
[3,1,5,4,2] => 1
[3,2,1,4,5] => 1
[3,2,1,5,4] => 1
[3,2,4,1,5] => 1
[3,2,4,5,1] => 1
[3,2,5,1,4] => 1
[3,2,5,4,1] => 2
[3,4,1,2,5] => 0
[3,4,1,5,2] => 0
[3,4,2,1,5] => 1
[3,4,2,5,1] => 1
[3,4,5,1,2] => 0
[3,4,5,2,1] => 1
[3,5,1,2,4] => 0
[3,5,1,4,2] => 0
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Description
The number of occurrences of the pattern 32-1.
See Permutations/#Pattern-avoiding_permutations for the definition of the pattern $32\!\!-\!\!1$.
See Permutations/#Pattern-avoiding_permutations for the definition of the pattern $32\!\!-\!\!1$.
Code
def statistic(pi):
n = len(pi)
return sum( 1 for j in range(2,n) for i in range(j-1) if pi[j] < pi[i+1] < pi[i] )
Created
Jan 13, 2016 at 12:06 by Christian Stump
Updated
May 10, 2019 at 17:27 by Henning Ulfarsson
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