- FindStat

Identifier

St001569: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

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

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Description

The maximal modular displacement of a permutation.
This is $\max_{1\leq i \leq n} \left(\min(\pi(i)-i\pmod n, i-\pi(i)\pmod n)\right)$ for a permutation $\pi$ of $\{1,\dots,n\}$.

References

[1] lemon314 Permutations with bounded displacement on a circle MathOverflow:366137

Code

def statistic(pi):
    n = len(pi)
    return max(min((e-1-i)%n,(i-e+1)%n) for i,e in enumerate(pi))

Created

Jul 21, 2020 at 21:37 by Martin Rubey

Updated

Jul 21, 2020 at 21:37 by Martin Rubey