Identifier
Values
0 => [1] => 1
1 => [1] => 1
00 => [2] => 1
01 => [1,1] => 1
10 => [1,1] => 1
11 => [2] => 1
000 => [3] => 1
001 => [2,1] => 1
010 => [1,1,1] => 1
011 => [1,2] => 1
100 => [1,2] => 1
101 => [1,1,1] => 1
110 => [2,1] => 1
111 => [3] => 1
0000 => [4] => 1
0001 => [3,1] => 1
0010 => [2,1,1] => 1
0011 => [2,2] => 2
0100 => [1,1,2] => 1
0101 => [1,1,1,1] => 2
0110 => [1,2,1] => 2
0111 => [1,3] => 1
1000 => [1,3] => 1
1001 => [1,2,1] => 2
1010 => [1,1,1,1] => 2
1011 => [1,1,2] => 1
1100 => [2,2] => 2
1101 => [2,1,1] => 1
1110 => [3,1] => 1
1111 => [4] => 1
00000 => [5] => 1
00001 => [4,1] => 1
00010 => [3,1,1] => 1
00011 => [3,2] => 1
00100 => [2,1,2] => 2
00101 => [2,1,1,1] => 1
00110 => [2,2,1] => 3
00111 => [2,3] => 2
01000 => [1,1,3] => 1
01001 => [1,1,2,1] => 2
01010 => [1,1,1,1,1] => 10
01011 => [1,1,1,2] => 3
01100 => [1,2,2] => 2
01101 => [1,2,1,1] => 2
01110 => [1,3,1] => 1
01111 => [1,4] => 1
10000 => [1,4] => 1
10001 => [1,3,1] => 1
10010 => [1,2,1,1] => 2
10011 => [1,2,2] => 2
10100 => [1,1,1,2] => 3
10101 => [1,1,1,1,1] => 10
10110 => [1,1,2,1] => 2
10111 => [1,1,3] => 1
11000 => [2,3] => 2
11001 => [2,2,1] => 3
11010 => [2,1,1,1] => 1
11011 => [2,1,2] => 2
11100 => [3,2] => 1
11101 => [3,1,1] => 1
11110 => [4,1] => 1
11111 => [5] => 1
000000 => [6] => 1
000001 => [5,1] => 1
000010 => [4,1,1] => 1
000011 => [4,2] => 2
000100 => [3,1,2] => 3
000101 => [3,1,1,1] => 1
000110 => [3,2,1] => 2
000111 => [3,3] => 2
001000 => [2,1,3] => 2
001001 => [2,1,2,1] => 4
001010 => [2,1,1,1,1] => 3
001011 => [2,1,1,2] => 1
001100 => [2,2,2] => 5
001101 => [2,2,1,1] => 3
001110 => [2,3,1] => 2
001111 => [2,4] => 2
010000 => [1,1,4] => 1
010001 => [1,1,3,1] => 3
010010 => [1,1,2,1,1] => 13
010011 => [1,1,2,2] => 3
010100 => [1,1,1,1,2] => 11
010101 => [1,1,1,1,1,1] => 53
010110 => [1,1,1,2,1] => 1
010111 => [1,1,1,3] => 3
011000 => [1,2,3] => 2
011001 => [1,2,2,1] => 6
011010 => [1,2,1,1,1] => 13
011011 => [1,2,1,2] => 3
011100 => [1,3,2] => 2
011101 => [1,3,1,1] => 4
011110 => [1,4,1] => 2
011111 => [1,5] => 1
100000 => [1,5] => 1
100001 => [1,4,1] => 2
100010 => [1,3,1,1] => 4
100011 => [1,3,2] => 2
100100 => [1,2,1,2] => 3
100101 => [1,2,1,1,1] => 13
100110 => [1,2,2,1] => 6
>>> Load all 254 entries. <<<
100111 => [1,2,3] => 2
101000 => [1,1,1,3] => 3
101001 => [1,1,1,2,1] => 1
101010 => [1,1,1,1,1,1] => 53
101011 => [1,1,1,1,2] => 11
101100 => [1,1,2,2] => 3
101101 => [1,1,2,1,1] => 13
101110 => [1,1,3,1] => 3
101111 => [1,1,4] => 1
110000 => [2,4] => 2
110001 => [2,3,1] => 2
110010 => [2,2,1,1] => 3
110011 => [2,2,2] => 5
110100 => [2,1,1,2] => 1
110101 => [2,1,1,1,1] => 3
110110 => [2,1,2,1] => 4
110111 => [2,1,3] => 2
111000 => [3,3] => 2
111001 => [3,2,1] => 2
111010 => [3,1,1,1] => 1
111011 => [3,1,2] => 3
111100 => [4,2] => 2
111101 => [4,1,1] => 1
111110 => [5,1] => 1
111111 => [6] => 1
0000000 => [7] => 1
0000001 => [6,1] => 1
0000010 => [5,1,1] => 1
0000011 => [5,2] => 1
0000100 => [4,1,2] => 2
0000101 => [4,1,1,1] => 1
0000110 => [4,2,1] => 2
0000111 => [4,3] => 2
0001000 => [3,1,3] => 3
0001001 => [3,1,2,1] => 2
0001010 => [3,1,1,1,1] => 3
0001011 => [3,1,1,2] => 3
0001100 => [3,2,2] => 3
0001101 => [3,2,1,1] => 2
0001110 => [3,3,1] => 4
0001111 => [3,4] => 2
0010000 => [2,1,4] => 2
0010001 => [2,1,3,1] => 3
0010010 => [2,1,2,1,1] => 14
0010011 => [2,1,2,2] => 6
0010100 => [2,1,1,1,2] => 4
0010101 => [2,1,1,1,1,1] => 11
0010110 => [2,1,1,2,1] => 3
0010111 => [2,1,1,3] => 1
0011000 => [2,2,3] => 6
0011001 => [2,2,2,1] => 8
0011010 => [2,2,1,1,1] => 3
0011011 => [2,2,1,2] => 5
0011100 => [2,3,2] => 3
0011101 => [2,3,1,1] => 2
0011110 => [2,4,1] => 2
0011111 => [2,5] => 2
0100000 => [1,1,5] => 1
0100001 => [1,1,4,1] => 2
0100010 => [1,1,3,1,1] => 9
0100011 => [1,1,3,2] => 6
0100100 => [1,1,2,1,2] => 16
0100101 => [1,1,2,1,1,1] => 42
0100110 => [1,1,2,2,1] => 5
0100111 => [1,1,2,3] => 3
0101000 => [1,1,1,1,3] => 11
0101001 => [1,1,1,1,2,1] => 4
0101010 => [1,1,1,1,1,1,1] => 589
0101011 => [1,1,1,1,1,2] => 61
0101100 => [1,1,1,2,2] => 3
0101101 => [1,1,1,2,1,1] => 53
0101110 => [1,1,1,3,1] => 3
0101111 => [1,1,1,4] => 3
0110000 => [1,2,4] => 2
0110001 => [1,2,3,1] => 3
0110010 => [1,2,2,1,1] => 9
0110011 => [1,2,2,2] => 9
0110100 => [1,2,1,1,2] => 16
0110101 => [1,2,1,1,1,1] => 40
0110110 => [1,2,1,2,1] => 16
0110111 => [1,2,1,3] => 4
0111000 => [1,3,3] => 2
0111001 => [1,3,2,1] => 3
0111010 => [1,3,1,1,1] => 10
0111011 => [1,3,1,2] => 5
0111100 => [1,4,2] => 2
0111101 => [1,4,1,1] => 2
0111110 => [1,5,1] => 1
0111111 => [1,6] => 1
1000000 => [1,6] => 1
1000001 => [1,5,1] => 1
1000010 => [1,4,1,1] => 2
1000011 => [1,4,2] => 2
1000100 => [1,3,1,2] => 5
1000101 => [1,3,1,1,1] => 10
1000110 => [1,3,2,1] => 3
1000111 => [1,3,3] => 2
1001000 => [1,2,1,3] => 4
1001001 => [1,2,1,2,1] => 16
1001010 => [1,2,1,1,1,1] => 40
1001011 => [1,2,1,1,2] => 16
1001100 => [1,2,2,2] => 9
1001101 => [1,2,2,1,1] => 9
1001110 => [1,2,3,1] => 3
1001111 => [1,2,4] => 2
1010000 => [1,1,1,4] => 3
1010001 => [1,1,1,3,1] => 3
1010010 => [1,1,1,2,1,1] => 53
1010011 => [1,1,1,2,2] => 3
1010100 => [1,1,1,1,1,2] => 61
1010101 => [1,1,1,1,1,1,1] => 589
1010110 => [1,1,1,1,2,1] => 4
1010111 => [1,1,1,1,3] => 11
1011000 => [1,1,2,3] => 3
1011001 => [1,1,2,2,1] => 5
1011010 => [1,1,2,1,1,1] => 42
1011011 => [1,1,2,1,2] => 16
1011100 => [1,1,3,2] => 6
1011101 => [1,1,3,1,1] => 9
1011110 => [1,1,4,1] => 2
1011111 => [1,1,5] => 1
1100000 => [2,5] => 2
1100001 => [2,4,1] => 2
1100010 => [2,3,1,1] => 2
1100011 => [2,3,2] => 3
1100100 => [2,2,1,2] => 5
1100101 => [2,2,1,1,1] => 3
1100110 => [2,2,2,1] => 8
1100111 => [2,2,3] => 6
1101000 => [2,1,1,3] => 1
1101001 => [2,1,1,2,1] => 3
1101010 => [2,1,1,1,1,1] => 11
1101011 => [2,1,1,1,2] => 4
1101100 => [2,1,2,2] => 6
1101101 => [2,1,2,1,1] => 14
1101110 => [2,1,3,1] => 3
1101111 => [2,1,4] => 2
1110000 => [3,4] => 2
1110001 => [3,3,1] => 4
1110010 => [3,2,1,1] => 2
1110011 => [3,2,2] => 3
1110100 => [3,1,1,2] => 3
1110101 => [3,1,1,1,1] => 3
1110110 => [3,1,2,1] => 2
1110111 => [3,1,3] => 3
1111000 => [4,3] => 2
1111001 => [4,2,1] => 2
1111010 => [4,1,1,1] => 1
1111011 => [4,1,2] => 2
1111100 => [5,2] => 1
1111101 => [5,1,1] => 1
1111110 => [6,1] => 1
1111111 => [7] => 1
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Description
The number of graphs with the given composition of multiplicities of Laplacian eigenvalues.
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 $w$.