Identifier
- St001640: Permutations ⟶ ℤ
Values
[1] => 0
[1,2] => 1
[2,1] => 0
[1,2,3] => 2
[1,3,2] => 0
[2,1,3] => 1
[2,3,1] => 0
[3,1,2] => 1
[3,2,1] => 0
[1,2,3,4] => 3
[1,2,4,3] => 1
[1,3,2,4] => 1
[1,3,4,2] => 0
[1,4,2,3] => 1
[1,4,3,2] => 0
[2,1,3,4] => 2
[2,1,4,3] => 0
[2,3,1,4] => 1
[2,3,4,1] => 0
[2,4,1,3] => 1
[2,4,3,1] => 0
[3,1,2,4] => 2
[3,1,4,2] => 0
[3,2,1,4] => 1
[3,2,4,1] => 0
[3,4,1,2] => 1
[3,4,2,1] => 0
[4,1,2,3] => 2
[4,1,3,2] => 0
[4,2,1,3] => 1
[4,2,3,1] => 0
[4,3,1,2] => 1
[4,3,2,1] => 0
[1,2,3,4,5] => 4
[1,2,3,5,4] => 2
[1,2,4,3,5] => 2
[1,2,4,5,3] => 1
[1,2,5,3,4] => 2
[1,2,5,4,3] => 1
[1,3,2,4,5] => 2
[1,3,2,5,4] => 0
[1,3,4,2,5] => 1
[1,3,4,5,2] => 0
[1,3,5,2,4] => 1
[1,3,5,4,2] => 0
[1,4,2,3,5] => 2
[1,4,2,5,3] => 0
[1,4,3,2,5] => 1
[1,4,3,5,2] => 0
[1,4,5,2,3] => 1
[1,4,5,3,2] => 0
[1,5,2,3,4] => 2
[1,5,2,4,3] => 0
[1,5,3,2,4] => 1
[1,5,3,4,2] => 0
[1,5,4,2,3] => 1
[1,5,4,3,2] => 0
[2,1,3,4,5] => 3
[2,1,3,5,4] => 1
[2,1,4,3,5] => 1
[2,1,4,5,3] => 0
[2,1,5,3,4] => 1
[2,1,5,4,3] => 0
[2,3,1,4,5] => 2
[2,3,1,5,4] => 0
[2,3,4,1,5] => 1
[2,3,4,5,1] => 0
[2,3,5,1,4] => 1
[2,3,5,4,1] => 0
[2,4,1,3,5] => 2
[2,4,1,5,3] => 0
[2,4,3,1,5] => 1
[2,4,3,5,1] => 0
[2,4,5,1,3] => 1
[2,4,5,3,1] => 0
[2,5,1,3,4] => 2
[2,5,1,4,3] => 0
[2,5,3,1,4] => 1
[2,5,3,4,1] => 0
[2,5,4,1,3] => 1
[2,5,4,3,1] => 0
[3,1,2,4,5] => 3
[3,1,2,5,4] => 1
[3,1,4,2,5] => 1
[3,1,4,5,2] => 0
[3,1,5,2,4] => 1
[3,1,5,4,2] => 0
[3,2,1,4,5] => 2
[3,2,1,5,4] => 0
[3,2,4,1,5] => 1
[3,2,4,5,1] => 0
[3,2,5,1,4] => 1
[3,2,5,4,1] => 0
[3,4,1,2,5] => 2
[3,4,1,5,2] => 0
[3,4,2,1,5] => 1
[3,4,2,5,1] => 0
[3,4,5,1,2] => 1
[3,4,5,2,1] => 0
[3,5,1,2,4] => 2
[3,5,1,4,2] => 0
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Description
The number of ascent tops in the permutation such that all smaller elements appear before.
Code
def statistic(p):
return sum(1 for i in range(len(p)-1) if p[i] < p[i+1] and set(range(1, p[i+1])).issubset(sorted(p[:i+1])))
Created
Nov 17, 2020 at 11:17 by Martin Rubey
Updated
Nov 17, 2020 at 11:17 by Martin Rubey
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