Identifier
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 $\{1,\dots,n\}$.
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.