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
011 => [1,2] => [1,0,1,1,0,0] => 2
100 => [1,2] => [1,0,1,1,0,0] => 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
0011 => [2,2] => [1,1,0,0,1,1,0,0] => 2
0110 => [1,2,1] => [1,0,1,1,0,0,1,0] => 3
0111 => [1,3] => [1,0,1,1,1,0,0,0] => 3
1000 => [1,3] => [1,0,1,1,1,0,0,0] => 3
1001 => [1,2,1] => [1,0,1,1,0,0,1,0] => 3
1100 => [2,2] => [1,1,0,0,1,1,0,0] => 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
00011 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 3
00111 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 4
01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 4
01111 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 4
10000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 4
10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 4
10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 4
11000 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
11001 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 3
11100 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 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
000011 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
000110 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
000111 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
001100 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
001110 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
001111 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
011000 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
011001 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
011100 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
011110 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
011111 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
100000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
100001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
100011 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
100110 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
100111 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
110000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
110001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
110011 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
111000 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
111001 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
111100 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 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
0000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
0000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
0000011 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
0000110 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
0000111 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
0001100 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
0001110 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
0001111 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
0011000 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
0011100 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
0011110 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
0011111 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
0110000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
0110001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
0110011 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
0111000 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
0111001 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
0111100 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
0111110 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
0111111 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
1000000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
1000001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
1000011 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
1000110 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
1000111 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
1001100 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
1001110 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
1001111 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
1100000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
1100001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
1100011 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
1100110 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
1100111 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
1110000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
1110001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
>>> Load all 106 entries. <<<
1111000 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
1111001 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
1111100 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
1111110 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
1111111 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
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 $w$.