Identifier
Values
00 => [2] => [1,1,0,0] => [1,2] => 0
01 => [1,1] => [1,0,1,0] => [2,1] => 1
10 => [1,1] => [1,0,1,0] => [2,1] => 1
11 => [2] => [1,1,0,0] => [1,2] => 0
000 => [3] => [1,1,1,0,0,0] => [1,2,3] => 0
001 => [2,1] => [1,1,0,0,1,0] => [1,3,2] => 1
010 => [1,1,1] => [1,0,1,0,1,0] => [2,3,1] => 1
011 => [1,2] => [1,0,1,1,0,0] => [2,1,3] => 1
100 => [1,2] => [1,0,1,1,0,0] => [2,1,3] => 1
101 => [1,1,1] => [1,0,1,0,1,0] => [2,3,1] => 1
110 => [2,1] => [1,1,0,0,1,0] => [1,3,2] => 1
111 => [3] => [1,1,1,0,0,0] => [1,2,3] => 0
0000 => [4] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 0
0001 => [3,1] => [1,1,1,0,0,0,1,0] => [1,2,4,3] => 1
0010 => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,3,4,2] => 2
0011 => [2,2] => [1,1,0,0,1,1,0,0] => [1,3,2,4] => 1
0100 => [1,1,2] => [1,0,1,0,1,1,0,0] => [2,3,1,4] => 2
0101 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 1
0110 => [1,2,1] => [1,0,1,1,0,0,1,0] => [2,1,4,3] => 1
0111 => [1,3] => [1,0,1,1,1,0,0,0] => [2,1,3,4] => 1
1000 => [1,3] => [1,0,1,1,1,0,0,0] => [2,1,3,4] => 1
1001 => [1,2,1] => [1,0,1,1,0,0,1,0] => [2,1,4,3] => 1
1010 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 1
1011 => [1,1,2] => [1,0,1,0,1,1,0,0] => [2,3,1,4] => 2
1100 => [2,2] => [1,1,0,0,1,1,0,0] => [1,3,2,4] => 1
1101 => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,3,4,2] => 2
1110 => [3,1] => [1,1,1,0,0,0,1,0] => [1,2,4,3] => 1
1111 => [4] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 0
00000 => [5] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => 0
00001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => 1
00010 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => 2
00011 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => 1
00100 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => 2
00101 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => 2
00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => 1
00111 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => 1
01000 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => 2
01001 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => 2
01010 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 1
01011 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => 2
01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => 1
01101 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => 2
01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => 1
01111 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => 1
10000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => 1
10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => 1
10010 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => 2
10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => 1
10100 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => 2
10101 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 1
10110 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => 2
10111 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => 2
11000 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => 1
11001 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => 1
11010 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => 2
11011 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => 2
11100 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => 1
11101 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => 2
11110 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => 1
11111 => [5] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => 0
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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
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.