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
11 => [1,1,1] => [1,0,1,0,1,0] => 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
011 => [2,1,1] => [1,1,0,0,1,0,1,0] => 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
110 => [1,1,2] => [1,0,1,0,1,1,0,0] => 3
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 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
0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 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
0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 3
0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 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
1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 4
1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 4
1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 4
1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 4
1111 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 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
00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 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
00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 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
01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 4
01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 4
01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 4
01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4
01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 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
10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 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
10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 5
10111 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 5
11000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 5
11001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 5
11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 5
11011 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 5
11100 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
11101 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 5
11110 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
11111 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
=> [1] => [1,0] => 0
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Description
The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra.
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.