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] => 3
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] => 3
010 => [2,2] => [1,1,0,0,1,1,0,0] => 3
011 => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
100 => [1,3] => [1,0,1,1,1,0,0,0] => 3
101 => [1,2,1] => [1,0,1,1,0,0,1,0] => 5
110 => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
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] => 3
0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 4
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] => 5
0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 4
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] => 3
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] => 4
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] => 5
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] => 3
00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
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] => 5
00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 4
00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 5
01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
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] => 4
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] => 5
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] => 3
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] => 7
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] => 6
11000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
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] => 7
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] => 6
11110 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
11111 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 7
000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
000010 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
000011 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 4
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] => 5
000110 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
000111 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5
001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
001001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 5
001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5
001011 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 5
001100 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
001101 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 5
001110 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 5
001111 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 6
010000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
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
010011 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 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] => 7
010110 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 5
010111 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 6
011000 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
011001 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 5
011010 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 5
011011 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 7
011100 => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 5
011101 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 6
011110 => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 6
011111 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
100000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
100001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
100010 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 5
100011 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 5
100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 7
100110 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 5
>>> Load all 127 entries. <<<
100111 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 6
101000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 5
101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 7
101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 7
101011 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 6
101100 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 5
101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 6
101110 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 6
101111 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7
110000 => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 4
110001 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 5
110010 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 5
110011 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 7
110100 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 5
110101 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 6
110110 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 7
110111 => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 7
111000 => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
111001 => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 6
111010 => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 6
111011 => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7
111100 => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
111101 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7
111110 => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
111111 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
=> [1] => [1,0] => 2
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Description
Number of indecomposable projective non-injective modules with dominant dimension equal to the global dimension plus the number of indecomposable projective injective modules in 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.