- FindStat

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Identifier

St001162: Permutations ⟶ ℤ

Values

[1,2] => 1

[2,1] => 1

[1,2,3] => 1

[1,3,2] => 1

[2,1,3] => 1

[2,3,1] => 1

[3,1,2] => 1

[3,2,1] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1199 entries. <<<

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$F_{2} = 2\ q$

$F_{3} = 6\ q$

$F_{4} = 22\ q + 2\ q^{2}$

$F_{5} = 106\ q + 14\ q^{2}$

$F_{6} = 630\ q + 88\ q^{2} + 2\ q^{3}$

Description

The minimum jump of a permutation.
This is

$\min_i |\pi_{i+1}-\pi_i|$ , see [1].

References

[1] Blackburn, S. R., Homberger, C., Winkler, P. The minimum Manhattan distance and minimum jump of permutations arXiv:1706.01557

Code

def statistic(pi):
    return min([abs(pi[i+1]-pi[i]) for i in range(len(pi)-1)])

Created

Apr 26, 2018 at 11:27 by Martin Rubey

Updated

Apr 26, 2018 at 11:27 by Martin Rubey