Identifier
Values
0 => [2] => [1,1,0,0] => 0
1 => [1,1] => [1,0,1,0] => 1
00 => [3] => [1,1,1,0,0,0] => 0
01 => [2,1] => [1,1,0,0,1,0] => 1
10 => [1,2] => [1,0,1,1,0,0] => 2
000 => [4] => [1,1,1,1,0,0,0,0] => 0
001 => [3,1] => [1,1,1,0,0,0,1,0] => 1
010 => [2,2] => [1,1,0,0,1,1,0,0] => 2
100 => [1,3] => [1,0,1,1,1,0,0,0] => 3
101 => [1,2,1] => [1,0,1,1,0,0,1,0] => 3
0000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 3
1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 4
1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 4
1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 4
00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
000010 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
000100 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
000101 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
001001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
010000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
010001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
100000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
100001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
100010 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
101000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
=> [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
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.