Identifier
-
Mp00231:
Integer compositions
—bounce path⟶
Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
St001569: Permutations ⟶ ℤ
Values
[1] => [1,0] => [2,1] => [2,1] => 1
[1,1] => [1,0,1,0] => [3,1,2] => [1,3,2] => 1
[2] => [1,1,0,0] => [2,3,1] => [2,1,3] => 1
[1,1,1] => [1,0,1,0,1,0] => [4,1,2,3] => [1,2,4,3] => 1
[1,2] => [1,0,1,1,0,0] => [3,1,4,2] => [3,1,4,2] => 2
[2,1] => [1,1,0,0,1,0] => [2,4,1,3] => [2,4,1,3] => 2
[3] => [1,1,1,0,0,0] => [2,3,4,1] => [2,1,3,4] => 1
[1,1,1,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [1,2,3,5,4] => 1
[1,1,2] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [4,1,2,5,3] => 2
[1,2,1] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [1,3,2,5,4] => 1
[1,3] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [3,1,4,5,2] => 2
[2,1,1] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [2,3,5,1,4] => 2
[2,2] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [2,1,4,3,5] => 1
[3,1] => [1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [2,5,1,3,4] => 2
[4] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [2,1,3,4,5] => 1
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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 $\{1,\dots,n\}$.
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 $\{1,\dots,n\}$.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
cactus evacuation
Description
The cactus evacuation of a permutation.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
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