Identifier
- St000694: Permutations ⟶ ℤ
Values
[1,2] => 4
[2,1] => 1
[1,2,3] => 8
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 2
[1,2,3,4] => 16
[1,2,4,3] => 4
[1,3,2,4] => 4
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 4
[2,1,3,4] => 4
[2,1,4,3] => 1
[2,3,1,4] => 2
[2,3,4,1] => 1
[2,4,1,3] => 1
[2,4,3,1] => 2
[3,1,2,4] => 2
[3,1,4,2] => 1
[3,2,1,4] => 4
[3,2,4,1] => 2
[3,4,1,2] => 1
[3,4,2,1] => 1
[4,1,2,3] => 1
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 4
[4,3,1,2] => 1
[4,3,2,1] => 1
[1,2,3,4,5] => 32
[1,2,3,5,4] => 8
[1,2,4,3,5] => 8
[1,2,4,5,3] => 4
[1,2,5,3,4] => 4
[1,2,5,4,3] => 8
[1,3,2,4,5] => 8
[1,3,2,5,4] => 2
[1,3,4,2,5] => 4
[1,3,4,5,2] => 2
[1,3,5,2,4] => 2
[1,3,5,4,2] => 4
[1,4,2,3,5] => 4
[1,4,2,5,3] => 2
[1,4,3,2,5] => 8
[1,4,3,5,2] => 4
[1,4,5,2,3] => 2
[1,4,5,3,2] => 2
[1,5,2,3,4] => 2
[1,5,2,4,3] => 4
[1,5,3,2,4] => 4
[1,5,3,4,2] => 8
[1,5,4,2,3] => 2
[1,5,4,3,2] => 2
[2,1,3,4,5] => 8
[2,1,3,5,4] => 2
[2,1,4,3,5] => 2
[2,1,4,5,3] => 1
[2,1,5,3,4] => 1
[2,1,5,4,3] => 2
[2,3,1,4,5] => 4
[2,3,1,5,4] => 1
[2,3,4,1,5] => 2
[2,3,4,5,1] => 1
[2,3,5,1,4] => 1
[2,3,5,4,1] => 2
[2,4,1,3,5] => 2
[2,4,1,5,3] => 1
[2,4,3,1,5] => 4
[2,4,3,5,1] => 2
[2,4,5,1,3] => 1
[2,4,5,3,1] => 1
[2,5,1,3,4] => 1
[2,5,1,4,3] => 2
[2,5,3,1,4] => 2
[2,5,3,4,1] => 4
[2,5,4,1,3] => 1
[2,5,4,3,1] => 1
[3,1,2,4,5] => 4
[3,1,2,5,4] => 1
[3,1,4,2,5] => 2
[3,1,4,5,2] => 1
[3,1,5,2,4] => 1
[3,1,5,4,2] => 2
[3,2,1,4,5] => 8
[3,2,1,5,4] => 2
[3,2,4,1,5] => 4
[3,2,4,5,1] => 2
[3,2,5,1,4] => 2
[3,2,5,4,1] => 4
[3,4,1,2,5] => 2
[3,4,1,5,2] => 1
[3,4,2,1,5] => 2
[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
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Description
The number of affine bounded permutations that project to a given permutation.
As affine bounded permutations are in bijection with usual permutations where fix-points come in two colors, this statistic is 2k where k is the number of fixed points St000022The number of fixed points of a permutation..
As affine bounded permutations are in bijection with usual permutations where fix-points come in two colors, this statistic is 2k where k is the number of fixed points St000022The number of fixed points of a permutation..
References
[1] Lam, T. Totally nonnegative Grassmannian and Grassmann polytopes arXiv:1506.00603
Code
def statistic(pi):
return 2^pi.number_of_fixed_points()
Created
Feb 03, 2017 at 11:11 by Christian Stump
Updated
Feb 03, 2017 at 11:11 by Christian Stump
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