Identifier
Values
0 => [1] => [1,0] => 0
1 => [1] => [1,0] => 0
00 => [2] => [1,1,0,0] => 0
01 => [1,1] => [1,0,1,0] => 1
10 => [1,1] => [1,0,1,0] => 1
11 => [2] => [1,1,0,0] => 0
000 => [3] => [1,1,1,0,0,0] => 0
001 => [2,1] => [1,1,0,0,1,0] => 1
010 => [1,1,1] => [1,0,1,0,1,0] => 2
011 => [1,2] => [1,0,1,1,0,0] => 1
100 => [1,2] => [1,0,1,1,0,0] => 1
101 => [1,1,1] => [1,0,1,0,1,0] => 2
110 => [2,1] => [1,1,0,0,1,0] => 1
111 => [3] => [1,1,1,0,0,0] => 0
0000 => [4] => [1,1,1,1,0,0,0,0] => 0
0001 => [3,1] => [1,1,1,0,0,0,1,0] => 1
0010 => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
0011 => [2,2] => [1,1,0,0,1,1,0,0] => 1
0100 => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
0101 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 3
0110 => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
0111 => [1,3] => [1,0,1,1,1,0,0,0] => 1
1000 => [1,3] => [1,0,1,1,1,0,0,0] => 1
1001 => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
1010 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 3
1011 => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
1100 => [2,2] => [1,1,0,0,1,1,0,0] => 1
1101 => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
1110 => [3,1] => [1,1,1,0,0,0,1,0] => 1
1111 => [4] => [1,1,1,1,0,0,0,0] => 0
00000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
00001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
00010 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
00011 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
00100 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
00101 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 3
00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
00111 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
01000 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
01001 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
01010 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 4
01011 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 3
01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
01101 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
01111 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
10000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
10010 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
10100 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 3
10101 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 4
10110 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
10111 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
11000 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
11001 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
11010 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 3
11011 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
11100 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
11101 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
11110 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
11111 => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
000000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
000001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
000010 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
000011 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
000100 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
000101 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
000110 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
000111 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
001000 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
001001 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
001010 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
001011 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
001100 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
001101 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
001110 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
001111 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
010000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
010001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
010010 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
010011 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
010100 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
010101 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
010110 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 3
010111 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
011000 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
011001 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 1
011010 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 3
011011 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
011100 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
011101 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
011110 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
011111 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
100000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
100001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
100010 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
100011 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
100100 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
100101 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 3
100110 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 1
>>> Load all 126 entries. <<<
100111 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
101000 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
101001 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 3
101010 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
101011 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
101100 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
101101 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
101110 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
101111 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
110000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
110001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
110010 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
110011 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
110100 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
110101 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
110110 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
110111 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
111000 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
111001 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
111010 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
111011 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
111100 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
111101 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
111110 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
111111 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
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Description
The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra.
See http://www.findstat.org/DyckPaths/NakayamaAlgebras.
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 $w$.
Map
bounce path
Description
The bounce path determined by an integer composition.