Identifier
Values
0 => [2] => [1,1,0,0] => 1
1 => [1,1] => [1,0,1,0] => 2
00 => [3] => [1,1,1,0,0,0] => 1
01 => [2,1] => [1,1,0,0,1,0] => 2
10 => [1,2] => [1,0,1,1,0,0] => 2
11 => [1,1,1] => [1,0,1,0,1,0] => 3
000 => [4] => [1,1,1,1,0,0,0,0] => 1
001 => [3,1] => [1,1,1,0,0,0,1,0] => 2
010 => [2,2] => [1,1,0,0,1,1,0,0] => 2
011 => [2,1,1] => [1,1,0,0,1,0,1,0] => 3
100 => [1,3] => [1,0,1,1,1,0,0,0] => 2
101 => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
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] => 4
0000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
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] => 3
0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
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] => 4
1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 3
1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
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] => 5
00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
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] => 3
00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
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] => 4
01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
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] => 5
10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
10111 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
11000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
11001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
11011 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3
11100 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
11101 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
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] => 6
=> [1] => [1,0] => 1
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Description
The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver.
The $k$-Gorenstein degree is the maximal number $k$ such that the algebra is $k$-Gorenstein. We apply the convention that the value is equal to the global dimension of the algebra in case the $k$-Gorenstein degree is greater than or equal to the global dimension.
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.