Identifier
- St000991: Permutations ⟶ ℤ
Values
[1] => 1
[1,2] => 2
[2,1] => 1
[1,2,3] => 3
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 1
[3,1,2] => 2
[3,2,1] => 1
[1,2,3,4] => 4
[1,2,4,3] => 3
[1,3,2,4] => 3
[1,3,4,2] => 2
[1,4,2,3] => 3
[1,4,3,2] => 2
[2,1,3,4] => 3
[2,1,4,3] => 2
[2,3,1,4] => 2
[2,3,4,1] => 1
[2,4,1,3] => 2
[2,4,3,1] => 1
[3,1,2,4] => 3
[3,1,4,2] => 2
[3,2,1,4] => 2
[3,2,4,1] => 1
[3,4,1,2] => 2
[3,4,2,1] => 1
[4,1,2,3] => 3
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 1
[4,3,1,2] => 2
[4,3,2,1] => 1
[1,2,3,4,5] => 5
[1,2,3,5,4] => 4
[1,2,4,3,5] => 4
[1,2,4,5,3] => 3
[1,2,5,3,4] => 4
[1,2,5,4,3] => 3
[1,3,2,4,5] => 4
[1,3,2,5,4] => 3
[1,3,4,2,5] => 3
[1,3,4,5,2] => 2
[1,3,5,2,4] => 3
[1,3,5,4,2] => 2
[1,4,2,3,5] => 4
[1,4,2,5,3] => 3
[1,4,3,2,5] => 3
[1,4,3,5,2] => 2
[1,4,5,2,3] => 3
[1,4,5,3,2] => 2
[1,5,2,3,4] => 4
[1,5,2,4,3] => 3
[1,5,3,2,4] => 3
[1,5,3,4,2] => 2
[1,5,4,2,3] => 3
[1,5,4,3,2] => 2
[2,1,3,4,5] => 4
[2,1,3,5,4] => 3
[2,1,4,3,5] => 3
[2,1,4,5,3] => 2
[2,1,5,3,4] => 3
[2,1,5,4,3] => 2
[2,3,1,4,5] => 3
[2,3,1,5,4] => 2
[2,3,4,1,5] => 2
[2,3,4,5,1] => 1
[2,3,5,1,4] => 2
[2,3,5,4,1] => 1
[2,4,1,3,5] => 3
[2,4,1,5,3] => 2
[2,4,3,1,5] => 2
[2,4,3,5,1] => 1
[2,4,5,1,3] => 2
[2,4,5,3,1] => 1
[2,5,1,3,4] => 3
[2,5,1,4,3] => 2
[2,5,3,1,4] => 2
[2,5,3,4,1] => 1
[2,5,4,1,3] => 2
[2,5,4,3,1] => 1
[3,1,2,4,5] => 4
[3,1,2,5,4] => 3
[3,1,4,2,5] => 3
[3,1,4,5,2] => 2
[3,1,5,2,4] => 3
[3,1,5,4,2] => 2
[3,2,1,4,5] => 3
[3,2,1,5,4] => 2
[3,2,4,1,5] => 2
[3,2,4,5,1] => 1
[3,2,5,1,4] => 2
[3,2,5,4,1] => 1
[3,4,1,2,5] => 3
[3,4,1,5,2] => 2
[3,4,2,1,5] => 2
[3,4,2,5,1] => 1
[3,4,5,1,2] => 2
[3,4,5,2,1] => 1
[3,5,1,2,4] => 3
[3,5,1,4,2] => 2
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Description
The number of right-to-left minima of a permutation.
For the number of left-to-right maxima, see St000314The number of left-to-right-maxima of a permutation..
For the number of left-to-right maxima, see St000314The number of left-to-right-maxima of a permutation..
Code
def rlmin(pi):
n = len(pi)
m = n+1
for i in range(n):
if pi[n-1-i] < m:
yield n-i
m = pi[n-1-i]
def statistic(pi):
return sum(1 for _ in rlmin(pi))
Created
Oct 17, 2017 at 17:57 by Jang Soo Kim
Updated
Oct 20, 2017 at 09:48 by Christian Stump
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