Identifier
Values
0 => [1] => 1
1 => [1] => 1
00 => [2] => 1
01 => [1,1] => 2
10 => [1,1] => 2
11 => [2] => 1
000 => [3] => 1
001 => [2,1] => 2
010 => [1,1,1] => 3
011 => [1,2] => 2
100 => [1,2] => 2
101 => [1,1,1] => 3
110 => [2,1] => 2
111 => [3] => 1
0000 => [4] => 1
0001 => [3,1] => 2
0010 => [2,1,1] => 3
0011 => [2,2] => 2
0100 => [1,1,2] => 3
0101 => [1,1,1,1] => 4
0110 => [1,2,1] => 2
0111 => [1,3] => 2
1000 => [1,3] => 2
1001 => [1,2,1] => 2
1010 => [1,1,1,1] => 4
1011 => [1,1,2] => 3
1100 => [2,2] => 2
1101 => [2,1,1] => 3
1110 => [3,1] => 2
1111 => [4] => 1
00000 => [5] => 1
00001 => [4,1] => 2
00010 => [3,1,1] => 3
00011 => [3,2] => 2
00100 => [2,1,2] => 3
00101 => [2,1,1,1] => 4
00110 => [2,2,1] => 2
00111 => [2,3] => 2
01000 => [1,1,3] => 3
01001 => [1,1,2,1] => 3
01010 => [1,1,1,1,1] => 5
01011 => [1,1,1,2] => 4
01100 => [1,2,2] => 2
01101 => [1,2,1,1] => 3
01110 => [1,3,1] => 2
01111 => [1,4] => 2
10000 => [1,4] => 2
10001 => [1,3,1] => 2
10010 => [1,2,1,1] => 3
10011 => [1,2,2] => 2
10100 => [1,1,1,2] => 4
10101 => [1,1,1,1,1] => 5
10110 => [1,1,2,1] => 3
10111 => [1,1,3] => 3
11000 => [2,3] => 2
11001 => [2,2,1] => 2
11010 => [2,1,1,1] => 4
11011 => [2,1,2] => 3
11100 => [3,2] => 2
11101 => [3,1,1] => 3
11110 => [4,1] => 2
11111 => [5] => 1
000000 => [6] => 1
000001 => [5,1] => 2
000010 => [4,1,1] => 3
000011 => [4,2] => 2
000100 => [3,1,2] => 3
000101 => [3,1,1,1] => 4
000110 => [3,2,1] => 2
000111 => [3,3] => 2
001000 => [2,1,3] => 3
001001 => [2,1,2,1] => 3
001010 => [2,1,1,1,1] => 5
001011 => [2,1,1,2] => 4
001100 => [2,2,2] => 2
001101 => [2,2,1,1] => 3
001110 => [2,3,1] => 2
001111 => [2,4] => 2
010000 => [1,1,4] => 3
010001 => [1,1,3,1] => 3
010010 => [1,1,2,1,1] => 3
010011 => [1,1,2,2] => 3
010100 => [1,1,1,1,2] => 5
010101 => [1,1,1,1,1,1] => 6
010110 => [1,1,1,2,1] => 4
010111 => [1,1,1,3] => 4
011000 => [1,2,3] => 2
011001 => [1,2,2,1] => 2
011010 => [1,2,1,1,1] => 4
011011 => [1,2,1,2] => 3
011100 => [1,3,2] => 2
011101 => [1,3,1,1] => 3
011110 => [1,4,1] => 2
011111 => [1,5] => 2
100000 => [1,5] => 2
100001 => [1,4,1] => 2
100010 => [1,3,1,1] => 3
100011 => [1,3,2] => 2
100100 => [1,2,1,2] => 3
100101 => [1,2,1,1,1] => 4
100110 => [1,2,2,1] => 2
>>> Load all 126 entries. <<<
100111 => [1,2,3] => 2
101000 => [1,1,1,3] => 4
101001 => [1,1,1,2,1] => 4
101010 => [1,1,1,1,1,1] => 6
101011 => [1,1,1,1,2] => 5
101100 => [1,1,2,2] => 3
101101 => [1,1,2,1,1] => 3
101110 => [1,1,3,1] => 3
101111 => [1,1,4] => 3
110000 => [2,4] => 2
110001 => [2,3,1] => 2
110010 => [2,2,1,1] => 3
110011 => [2,2,2] => 2
110100 => [2,1,1,2] => 4
110101 => [2,1,1,1,1] => 5
110110 => [2,1,2,1] => 3
110111 => [2,1,3] => 3
111000 => [3,3] => 2
111001 => [3,2,1] => 2
111010 => [3,1,1,1] => 4
111011 => [3,1,2] => 3
111100 => [4,2] => 2
111101 => [4,1,1] => 3
111110 => [5,1] => 2
111111 => [6] => 1
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Description
The global dimension of the corresponding Comp-Nakayama algebra.
We identify the composition [n1-1,n2-1,...,nr-1] with the Nakayama algebra with Kupisch series [n1,n1-1,...,2,n2,n2-1,...,2,...,nr,nr-1,...,3,2,1]. We call such Nakayama algebras with Kupisch series corresponding to a integer composition "Comp-Nakayama algebra".
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.