Identifier
Values
0 => [2] => [1,1,0,0] => 3
1 => [1,1] => [1,0,1,0] => 3
00 => [3] => [1,1,1,0,0,0] => 4
01 => [2,1] => [1,1,0,0,1,0] => 3
10 => [1,2] => [1,0,1,1,0,0] => 4
11 => [1,1,1] => [1,0,1,0,1,0] => 4
000 => [4] => [1,1,1,1,0,0,0,0] => 5
001 => [3,1] => [1,1,1,0,0,0,1,0] => 4
010 => [2,2] => [1,1,0,0,1,1,0,0] => 4
011 => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
100 => [1,3] => [1,0,1,1,1,0,0,0] => 5
101 => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
110 => [1,1,2] => [1,0,1,0,1,1,0,0] => 5
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 5
0000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 6
0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 5
0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 5
0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 5
0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 4
0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 6
1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 5
1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 6
1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 6
1111 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 6
00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 6
00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 6
00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 5
00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 6
00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 6
01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 5
01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 5
01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 5
01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 6
01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 5
01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 6
10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 6
10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
10111 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
11000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 7
11001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 6
11011 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
11100 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 7
11101 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
11110 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 7
11111 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 7
=> [1] => [1,0] => 2
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Description
The number of simple modules with injective dimension at most one or dominant dimension at least one.
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.