Identifier
Values
0 => 1 => [1] => 1
1 => 1 => [1] => 1
00 => 01 => [1,1] => 2
01 => 10 => [1,1] => 2
10 => 11 => [2] => 1
11 => 11 => [2] => 1
000 => 001 => [2,1] => 2
001 => 010 => [1,1,1] => 3
010 => 101 => [1,1,1] => 3
011 => 101 => [1,1,1] => 3
100 => 101 => [1,1,1] => 3
101 => 110 => [2,1] => 2
110 => 111 => [3] => 1
111 => 111 => [3] => 1
0000 => 0001 => [3,1] => 2
0001 => 0010 => [2,1,1] => 3
0010 => 0101 => [1,1,1,1] => 4
0011 => 0101 => [1,1,1,1] => 4
0100 => 1001 => [1,2,1] => 2
0101 => 1010 => [1,1,1,1] => 4
0110 => 1011 => [1,1,2] => 3
0111 => 1011 => [1,1,2] => 3
1000 => 1001 => [1,2,1] => 2
1001 => 1010 => [1,1,1,1] => 4
1010 => 1101 => [2,1,1] => 3
1011 => 1101 => [2,1,1] => 3
1100 => 1101 => [2,1,1] => 3
1101 => 1110 => [3,1] => 2
1110 => 1111 => [4] => 1
1111 => 1111 => [4] => 1
00000 => 00001 => [4,1] => 2
00001 => 00010 => [3,1,1] => 3
00010 => 00101 => [2,1,1,1] => 4
00011 => 00101 => [2,1,1,1] => 4
00100 => 01001 => [1,1,2,1] => 3
00101 => 01010 => [1,1,1,1,1] => 5
00110 => 01011 => [1,1,1,2] => 4
00111 => 01011 => [1,1,1,2] => 4
01000 => 10001 => [1,3,1] => 2
01001 => 10010 => [1,2,1,1] => 3
01010 => 10101 => [1,1,1,1,1] => 5
01011 => 10101 => [1,1,1,1,1] => 5
01100 => 10101 => [1,1,1,1,1] => 5
01101 => 10110 => [1,1,2,1] => 3
01110 => 10111 => [1,1,3] => 3
01111 => 10111 => [1,1,3] => 3
10000 => 10001 => [1,3,1] => 2
10001 => 10010 => [1,2,1,1] => 3
10010 => 10101 => [1,1,1,1,1] => 5
10011 => 10101 => [1,1,1,1,1] => 5
10100 => 11001 => [2,2,1] => 2
10101 => 11010 => [2,1,1,1] => 4
10110 => 11011 => [2,1,2] => 3
10111 => 11011 => [2,1,2] => 3
11000 => 11001 => [2,2,1] => 2
11001 => 11010 => [2,1,1,1] => 4
11010 => 11101 => [3,1,1] => 3
11011 => 11101 => [3,1,1] => 3
11100 => 11101 => [3,1,1] => 3
11101 => 11110 => [4,1] => 2
11110 => 11111 => [5] => 1
11111 => 11111 => [5] => 1
000000 => 000001 => [5,1] => 2
000001 => 000010 => [4,1,1] => 3
000010 => 000101 => [3,1,1,1] => 4
000011 => 000101 => [3,1,1,1] => 4
000100 => 001001 => [2,1,2,1] => 3
000101 => 001010 => [2,1,1,1,1] => 5
000110 => 001011 => [2,1,1,2] => 4
000111 => 001011 => [2,1,1,2] => 4
001000 => 010001 => [1,1,3,1] => 3
001001 => 010010 => [1,1,2,1,1] => 3
001010 => 010101 => [1,1,1,1,1,1] => 6
001011 => 010101 => [1,1,1,1,1,1] => 6
001100 => 010101 => [1,1,1,1,1,1] => 6
001101 => 010110 => [1,1,1,2,1] => 4
001110 => 010111 => [1,1,1,3] => 4
001111 => 010111 => [1,1,1,3] => 4
010000 => 100001 => [1,4,1] => 2
010001 => 100010 => [1,3,1,1] => 3
010010 => 100101 => [1,2,1,1,1] => 4
010011 => 100101 => [1,2,1,1,1] => 4
010100 => 101001 => [1,1,1,2,1] => 4
010101 => 101010 => [1,1,1,1,1,1] => 6
010110 => 101011 => [1,1,1,1,2] => 5
010111 => 101011 => [1,1,1,1,2] => 5
011000 => 101001 => [1,1,1,2,1] => 4
011001 => 101010 => [1,1,1,1,1,1] => 6
011010 => 101101 => [1,1,2,1,1] => 3
011011 => 101101 => [1,1,2,1,1] => 3
011100 => 101101 => [1,1,2,1,1] => 3
011101 => 101110 => [1,1,3,1] => 3
011110 => 101111 => [1,1,4] => 3
011111 => 101111 => [1,1,4] => 3
100000 => 100001 => [1,4,1] => 2
100001 => 100010 => [1,3,1,1] => 3
100010 => 100101 => [1,2,1,1,1] => 4
100011 => 100101 => [1,2,1,1,1] => 4
100100 => 101001 => [1,1,1,2,1] => 4
100101 => 101010 => [1,1,1,1,1,1] => 6
100110 => 101011 => [1,1,1,1,2] => 5
>>> Load all 126 entries. <<<
100111 => 101011 => [1,1,1,1,2] => 5
101000 => 110001 => [2,3,1] => 2
101001 => 110010 => [2,2,1,1] => 3
101010 => 110101 => [2,1,1,1,1] => 5
101011 => 110101 => [2,1,1,1,1] => 5
101100 => 110101 => [2,1,1,1,1] => 5
101101 => 110110 => [2,1,2,1] => 3
101110 => 110111 => [2,1,3] => 3
101111 => 110111 => [2,1,3] => 3
110000 => 110001 => [2,3,1] => 2
110001 => 110010 => [2,2,1,1] => 3
110010 => 110101 => [2,1,1,1,1] => 5
110011 => 110101 => [2,1,1,1,1] => 5
110100 => 111001 => [3,2,1] => 2
110101 => 111010 => [3,1,1,1] => 4
110110 => 111011 => [3,1,2] => 3
110111 => 111011 => [3,1,2] => 3
111000 => 111001 => [3,2,1] => 2
111001 => 111010 => [3,1,1,1] => 4
111010 => 111101 => [4,1,1] => 3
111011 => 111101 => [4,1,1] => 3
111100 => 111101 => [4,1,1] => 3
111101 => 111110 => [5,1] => 2
111110 => 111111 => [6] => 1
111111 => 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
valleys-to-peaks
Description
Return the binary word with every valley replaced by a peak.
A valley in a binary word is a subsequence $01$, or a trailing $0$. A peak is a subsequence $10$ or a trailing $1$. This map replaces every valley with a peak.
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 $w$.