- FindStat

Identifier

St001948: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1,2]=>1
[2,1]=>0
[1,2,3]=>2
[1,3,2]=>1
[2,1,3]=>0
[2,3,1]=>1
[3,1,2]=>0
[3,2,1]=>0
[1,2,3,4]=>3
[1,2,4,3]=>2
[1,3,2,4]=>1
[1,3,4,2]=>2
[1,4,2,3]=>1
[1,4,3,2]=>1
[2,1,3,4]=>1
[2,1,4,3]=>0
[2,3,1,4]=>1
[2,3,4,1]=>2
[2,4,1,3]=>1
[2,4,3,1]=>1
[3,1,2,4]=>1
[3,1,4,2]=>0
[3,2,1,4]=>0
[3,2,4,1]=>0
[3,4,1,2]=>1
[3,4,2,1]=>1
[4,1,2,3]=>1
[4,1,3,2]=>0
[4,2,1,3]=>0
[4,2,3,1]=>0
[4,3,1,2]=>0
[4,3,2,1]=>0
[1,2,3,4,5]=>4
[1,2,3,5,4]=>3
[1,2,4,3,5]=>2
[1,2,4,5,3]=>3
[1,2,5,3,4]=>2
[1,2,5,4,3]=>2
[1,3,2,4,5]=>2
[1,3,2,5,4]=>1
[1,3,4,2,5]=>2
[1,3,4,5,2]=>3
[1,3,5,2,4]=>2
[1,3,5,4,2]=>2
[1,4,2,3,5]=>2
[1,4,2,5,3]=>1
[1,4,3,2,5]=>1
[1,4,3,5,2]=>1
[1,4,5,2,3]=>2
[1,4,5,3,2]=>2
[1,5,2,3,4]=>2
[1,5,2,4,3]=>1
[1,5,3,2,4]=>1
[1,5,3,4,2]=>1
[1,5,4,2,3]=>1
[1,5,4,3,2]=>1
[2,1,3,4,5]=>2
[2,1,3,5,4]=>1
[2,1,4,3,5]=>0
[2,1,4,5,3]=>1
[2,1,5,3,4]=>0
[2,1,5,4,3]=>0
[2,3,1,4,5]=>2
[2,3,1,5,4]=>1
[2,3,4,1,5]=>2
[2,3,4,5,1]=>3
[2,3,5,1,4]=>2
[2,3,5,4,1]=>2
[2,4,1,3,5]=>2
[2,4,1,5,3]=>1
[2,4,3,1,5]=>1
[2,4,3,5,1]=>1
[2,4,5,1,3]=>2
[2,4,5,3,1]=>2
[2,5,1,3,4]=>2
[2,5,1,4,3]=>1
[2,5,3,1,4]=>1
[2,5,3,4,1]=>1
[2,5,4,1,3]=>1
[2,5,4,3,1]=>1
[3,1,2,4,5]=>2
[3,1,2,5,4]=>1
[3,1,4,2,5]=>0
[3,1,4,5,2]=>1
[3,1,5,2,4]=>0
[3,1,5,4,2]=>0
[3,2,1,4,5]=>1
[3,2,1,5,4]=>0
[3,2,4,1,5]=>0
[3,2,4,5,1]=>1
[3,2,5,1,4]=>0
[3,2,5,4,1]=>0
[3,4,1,2,5]=>2
[3,4,1,5,2]=>1
[3,4,2,1,5]=>1
[3,4,2,5,1]=>1
[3,4,5,1,2]=>2
[3,4,5,2,1]=>2
[3,5,1,2,4]=>2
[3,5,1,4,2]=>1
[3,5,2,1,4]=>1
[3,5,2,4,1]=>1
[3,5,4,1,2]=>1
[3,5,4,2,1]=>1
[4,1,2,3,5]=>2
[4,1,2,5,3]=>1
[4,1,3,2,5]=>0
[4,1,3,5,2]=>1
[4,1,5,2,3]=>0
[4,1,5,3,2]=>0
[4,2,1,3,5]=>1
[4,2,1,5,3]=>0
[4,2,3,1,5]=>0
[4,2,3,5,1]=>1
[4,2,5,1,3]=>0
[4,2,5,3,1]=>0
[4,3,1,2,5]=>1
[4,3,1,5,2]=>0
[4,3,2,1,5]=>0
[4,3,2,5,1]=>0
[4,3,5,1,2]=>0
[4,3,5,2,1]=>0
[4,5,1,2,3]=>2
[4,5,1,3,2]=>1
[4,5,2,1,3]=>1
[4,5,2,3,1]=>1
[4,5,3,1,2]=>1
[4,5,3,2,1]=>1
[5,1,2,3,4]=>2
[5,1,2,4,3]=>1
[5,1,3,2,4]=>0
[5,1,3,4,2]=>1
[5,1,4,2,3]=>0
[5,1,4,3,2]=>0
[5,2,1,3,4]=>1
[5,2,1,4,3]=>0
[5,2,3,1,4]=>0
[5,2,3,4,1]=>1
[5,2,4,1,3]=>0
[5,2,4,3,1]=>0
[5,3,1,2,4]=>1
[5,3,1,4,2]=>0
[5,3,2,1,4]=>0
[5,3,2,4,1]=>0
[5,3,4,1,2]=>0
[5,3,4,2,1]=>0
[5,4,1,2,3]=>1
[5,4,1,3,2]=>0
[5,4,2,1,3]=>0
[5,4,2,3,1]=>0
[5,4,3,1,2]=>0
[5,4,3,2,1]=>0
                    

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Description

The number of augmented double ascents of a permutation.
An augmented double ascent of a permutation $\pi$ is a double ascent of the augmented permutation $\tilde\pi$ obtained from $\pi$ by adding an initial $0$.
A double ascent of $\tilde\pi$ then is a position $i$ such that $\tilde\pi(i) < \tilde\pi(i+1) < \tilde\pi(i+2)$.

Code

def statistic(pi):
    pi = [0] + list(pi)
    return sum(1 for i in range(1,len(pi)-1) if pi[i-1] < pi[i] < pi[i+1])

Created

Jul 03, 2024 at 11:46 by Elena Hoster

Updated

Jul 04, 2024 at 09:15 by Christian Stump