Identifier
Values
0 => [2] => [1,1,0,0] => [2,3,1] => 1
1 => [1,1] => [1,0,1,0] => [3,1,2] => 1
00 => [3] => [1,1,1,0,0,0] => [2,3,4,1] => 1
01 => [2,1] => [1,1,0,0,1,0] => [2,4,1,3] => 2
10 => [1,2] => [1,0,1,1,0,0] => [3,1,4,2] => 2
11 => [1,1,1] => [1,0,1,0,1,0] => [4,1,2,3] => 1
000 => [4] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
001 => [3,1] => [1,1,1,0,0,0,1,0] => [2,3,5,1,4] => 2
010 => [2,2] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => 2
011 => [2,1,1] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => 2
100 => [1,3] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 2
101 => [1,2,1] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => 2
110 => [1,1,2] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 2
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
=> [1] => [1,0] => [2,1] => 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
bounce path
Description
The bounce path determined by an integer composition.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.