Identifier
- St001766: Permutations ⟶ ℤ
Values
[1] => 0
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 2
[2,1,3] => 0
[2,3,1] => 0
[3,1,2] => 0
[3,2,1] => 0
[1,2,3,4] => 0
[1,2,4,3] => 3
[1,3,2,4] => 2
[1,3,4,2] => 4
[1,4,2,3] => 4
[1,4,3,2] => 5
[2,1,3,4] => 0
[2,1,4,3] => 3
[2,3,1,4] => 0
[2,3,4,1] => 0
[2,4,1,3] => 2
[2,4,3,1] => 2
[3,1,2,4] => 0
[3,1,4,2] => 2
[3,2,1,4] => 0
[3,2,4,1] => 0
[3,4,1,2] => 0
[3,4,2,1] => 0
[4,1,2,3] => 0
[4,1,3,2] => 2
[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] => 0
[1,2,3,5,4] => 4
[1,2,4,3,5] => 3
[1,2,4,5,3] => 6
[1,2,5,3,4] => 6
[1,2,5,4,3] => 7
[1,3,2,4,5] => 2
[1,3,2,5,4] => 6
[1,3,4,2,5] => 4
[1,3,4,5,2] => 6
[1,3,5,2,4] => 7
[1,3,5,4,2] => 8
[1,4,2,3,5] => 4
[1,4,2,5,3] => 7
[1,4,3,2,5] => 5
[1,4,3,5,2] => 7
[1,4,5,2,3] => 7
[1,4,5,3,2] => 8
[1,5,2,3,4] => 6
[1,5,2,4,3] => 8
[1,5,3,2,4] => 7
[1,5,3,4,2] => 9
[1,5,4,2,3] => 8
[1,5,4,3,2] => 9
[2,1,3,4,5] => 0
[2,1,3,5,4] => 4
[2,1,4,3,5] => 3
[2,1,4,5,3] => 6
[2,1,5,3,4] => 6
[2,1,5,4,3] => 7
[2,3,1,4,5] => 0
[2,3,1,5,4] => 4
[2,3,4,1,5] => 0
[2,3,4,5,1] => 0
[2,3,5,1,4] => 3
[2,3,5,4,1] => 3
[2,4,1,3,5] => 2
[2,4,1,5,3] => 5
[2,4,3,1,5] => 2
[2,4,3,5,1] => 2
[2,4,5,1,3] => 4
[2,4,5,3,1] => 4
[2,5,1,3,4] => 4
[2,5,1,4,3] => 6
[2,5,3,1,4] => 4
[2,5,3,4,1] => 4
[2,5,4,1,3] => 5
[2,5,4,3,1] => 5
[3,1,2,4,5] => 0
[3,1,2,5,4] => 4
[3,1,4,2,5] => 2
[3,1,4,5,2] => 4
[3,1,5,2,4] => 5
[3,1,5,4,2] => 6
[3,2,1,4,5] => 0
[3,2,1,5,4] => 4
[3,2,4,1,5] => 0
[3,2,4,5,1] => 0
[3,2,5,1,4] => 3
[3,2,5,4,1] => 3
[3,4,1,2,5] => 0
[3,4,1,5,2] => 2
[3,4,2,1,5] => 0
[3,4,2,5,1] => 0
[3,4,5,1,2] => 0
[3,4,5,2,1] => 0
[3,5,1,2,4] => 2
[3,5,1,4,2] => 4
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Description
The number of cells which are not occupied by the same tile in all reduced pipe dreams corresponding to a permutation.
Precisely the 132-avoiding permutations have only one associated reduced pipe dream.
Precisely the 132-avoiding permutations have only one associated reduced pipe dream.
References
[1] Bergeron, N., Billey, S. RC-graphs and Schubert polynomials MathSciNet:1281474
Created
Jan 22, 2022 at 12:00 by Martin Rubey
Updated
Jan 22, 2022 at 12:10 by Martin Rubey
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