Identifier
Values
0 => 1 => [1,1] => [1,0,1,0] => 1
1 => 0 => [2] => [1,1,0,0] => 0
01 => 10 => [1,2] => [1,0,1,1,0,0] => 2
10 => 01 => [2,1] => [1,1,0,0,1,0] => 1
11 => 00 => [3] => [1,1,1,0,0,0] => 0
010 => 101 => [1,2,1] => [1,0,1,1,0,0,1,0] => 3
011 => 100 => [1,3] => [1,0,1,1,1,0,0,0] => 3
101 => 010 => [2,2] => [1,1,0,0,1,1,0,0] => 2
110 => 001 => [3,1] => [1,1,1,0,0,0,1,0] => 1
111 => 000 => [4] => [1,1,1,1,0,0,0,0] => 0
0101 => 1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 4
0110 => 1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 4
0111 => 1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 4
1010 => 0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 3
1011 => 0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
1101 => 0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
1110 => 0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
1111 => 0000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
01010 => 10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
01011 => 10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
01101 => 10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
01110 => 10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
01111 => 10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
10101 => 01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
10110 => 01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
10111 => 01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
11010 => 00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
11011 => 00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
11101 => 00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
11110 => 00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
11111 => 00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
010101 => 101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
010110 => 101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
010111 => 101000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
011010 => 100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
011011 => 100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
011101 => 100010 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
011110 => 100001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
011111 => 100000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
101010 => 010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
101011 => 010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
101101 => 010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
101110 => 010001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
101111 => 010000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
110101 => 001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
110110 => 001001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
110111 => 001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
111010 => 000101 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
111011 => 000100 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
111101 => 000010 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
111110 => 000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
111111 => 000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
=> => [1] => [1,0] => 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
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
bounce path
Description
The bounce path determined by an integer composition.
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.