Identifier
- St001807: Permutations ⟶ ℤ
Values
[1] => 1
[1,2] => 1
[2,1] => 2
[1,2,3] => 2
[1,3,2] => 3
[2,1,3] => 1
[2,3,1] => 3
[3,1,2] => 1
[3,2,1] => 2
[1,2,3,4] => 2
[1,2,4,3] => 2
[1,3,2,4] => 3
[1,3,4,2] => 3
[1,4,2,3] => 4
[1,4,3,2] => 4
[2,1,3,4] => 1
[2,1,4,3] => 1
[2,3,1,4] => 3
[2,3,4,1] => 3
[2,4,1,3] => 4
[2,4,3,1] => 4
[3,1,2,4] => 1
[3,1,4,2] => 1
[3,2,1,4] => 2
[3,2,4,1] => 2
[3,4,1,2] => 4
[3,4,2,1] => 4
[4,1,2,3] => 1
[4,1,3,2] => 1
[4,2,1,3] => 2
[4,2,3,1] => 2
[4,3,1,2] => 3
[4,3,2,1] => 3
[1,2,3,4,5] => 3
[1,2,3,5,4] => 3
[1,2,4,3,5] => 4
[1,2,4,5,3] => 4
[1,2,5,3,4] => 5
[1,2,5,4,3] => 5
[1,3,2,4,5] => 2
[1,3,2,5,4] => 2
[1,3,4,2,5] => 4
[1,3,4,5,2] => 4
[1,3,5,2,4] => 5
[1,3,5,4,2] => 5
[1,4,2,3,5] => 2
[1,4,2,5,3] => 2
[1,4,3,2,5] => 3
[1,4,3,5,2] => 3
[1,4,5,2,3] => 5
[1,4,5,3,2] => 5
[1,5,2,3,4] => 2
[1,5,2,4,3] => 2
[1,5,3,2,4] => 3
[1,5,3,4,2] => 3
[1,5,4,2,3] => 4
[1,5,4,3,2] => 4
[2,1,3,4,5] => 3
[2,1,3,5,4] => 3
[2,1,4,3,5] => 4
[2,1,4,5,3] => 4
[2,1,5,3,4] => 5
[2,1,5,4,3] => 5
[2,3,1,4,5] => 1
[2,3,1,5,4] => 1
[2,3,4,1,5] => 4
[2,3,4,5,1] => 4
[2,3,5,1,4] => 5
[2,3,5,4,1] => 5
[2,4,1,3,5] => 1
[2,4,1,5,3] => 1
[2,4,3,1,5] => 3
[2,4,3,5,1] => 3
[2,4,5,1,3] => 5
[2,4,5,3,1] => 5
[2,5,1,3,4] => 1
[2,5,1,4,3] => 1
[2,5,3,1,4] => 3
[2,5,3,4,1] => 3
[2,5,4,1,3] => 4
[2,5,4,3,1] => 4
[3,1,2,4,5] => 2
[3,1,2,5,4] => 2
[3,1,4,2,5] => 4
[3,1,4,5,2] => 4
[3,1,5,2,4] => 5
[3,1,5,4,2] => 5
[3,2,1,4,5] => 1
[3,2,1,5,4] => 1
[3,2,4,1,5] => 4
[3,2,4,5,1] => 4
[3,2,5,1,4] => 5
[3,2,5,4,1] => 5
[3,4,1,2,5] => 1
[3,4,1,5,2] => 1
[3,4,2,1,5] => 2
[3,4,2,5,1] => 2
[3,4,5,1,2] => 5
[3,4,5,2,1] => 5
[3,5,1,2,4] => 1
[3,5,1,4,2] => 1
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Description
The lower middle entry of a permutation.
This is the entry $\sigma(\frac{n+1}{2})$ when $n$ is odd, and $\sigma(\frac{n}{2})$ when $n$ is even, where $n$ is the size of the permutation $\sigma$.
This is the entry $\sigma(\frac{n+1}{2})$ when $n$ is odd, and $\sigma(\frac{n}{2})$ when $n$ is even, where $n$ is the size of the permutation $\sigma$.
Code
def statistic(p):
n = p.size()
return p(int((n+1)/2))
Created
Jun 10, 2022 at 17:24 by Nadia Lafreniere
Updated
Jun 10, 2022 at 17:24 by Nadia Lafreniere
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