Processing math: 100%

Identifier
Values
0 => 1 => [1,1] => [1,0,1,0] => 1
1 => 0 => [2] => [1,1,0,0] => 0
01 => 10 => [1,2] => [1,0,1,1,0,0] => 2
10 => 01 => [2,1] => [1,1,0,0,1,0] => 1
11 => 00 => [3] => [1,1,1,0,0,0] => 0
010 => 101 => [1,2,1] => [1,0,1,1,0,0,1,0] => 3
011 => 100 => [1,3] => [1,0,1,1,1,0,0,0] => 3
101 => 010 => [2,2] => [1,1,0,0,1,1,0,0] => 2
110 => 001 => [3,1] => [1,1,1,0,0,0,1,0] => 1
111 => 000 => [4] => [1,1,1,1,0,0,0,0] => 0
0101 => 1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 4
0110 => 1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 4
0111 => 1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 4
1010 => 0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 3
1011 => 0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
1101 => 0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
1110 => 0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
1111 => 0000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
01010 => 10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
01011 => 10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
01101 => 10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
01110 => 10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
01111 => 10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
10101 => 01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
10110 => 01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
10111 => 01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
11010 => 00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
11011 => 00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
11101 => 00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
11110 => 00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
11111 => 00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
010101 => 101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
010110 => 101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
010111 => 101000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
011010 => 100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
011011 => 100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
011101 => 100010 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
011110 => 100001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
011111 => 100000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
101010 => 010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
101011 => 010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
101101 => 010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
101110 => 010001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
101111 => 010000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
110101 => 001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
110110 => 001001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
110111 => 001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
111010 => 000101 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
111011 => 000100 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
111101 => 000010 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
111110 => 000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
111111 => 000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
=> => [1] => [1,0] => 0
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Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.
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.