Identifier
-
Mp00097:
Binary words
—delta morphism⟶
Integer compositions
St000757: Integer compositions ⟶ ℤ
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] => 1
010 => [1,1,1] => 3
011 => [1,2] => 2
100 => [1,2] => 2
101 => [1,1,1] => 3
110 => [2,1] => 1
111 => [3] => 1
0000 => [4] => 1
0001 => [3,1] => 1
0010 => [2,1,1] => 2
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] => 2
1110 => [3,1] => 1
1111 => [4] => 1
00000 => [5] => 1
00001 => [4,1] => 1
00010 => [3,1,1] => 2
00011 => [3,2] => 1
00100 => [2,1,2] => 2
00101 => [2,1,1,1] => 3
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] => 3
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] => 3
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] => 3
11011 => [2,1,2] => 2
11100 => [3,2] => 1
11101 => [3,1,1] => 2
11110 => [4,1] => 1
11111 => [5] => 1
000000 => [6] => 1
000001 => [5,1] => 1
000010 => [4,1,1] => 2
000011 => [4,2] => 1
000100 => [3,1,2] => 2
000101 => [3,1,1,1] => 3
000110 => [3,2,1] => 1
000111 => [3,3] => 2
001000 => [2,1,3] => 2
001001 => [2,1,2,1] => 2
001010 => [2,1,1,1,1] => 4
001011 => [2,1,1,2] => 3
001100 => [2,2,2] => 3
001101 => [2,2,1,1] => 2
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] => 4
010011 => [1,1,2,2] => 4
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] => 3
011001 => [1,2,2,1] => 3
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] => 3
>>> Load all 1022 entries. <<<100111 => [1,2,3] => 3
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] => 4
101101 => [1,1,2,1,1] => 4
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] => 2
110011 => [2,2,2] => 3
110100 => [2,1,1,2] => 3
110101 => [2,1,1,1,1] => 4
110110 => [2,1,2,1] => 2
110111 => [2,1,3] => 2
111000 => [3,3] => 2
111001 => [3,2,1] => 1
111010 => [3,1,1,1] => 3
111011 => [3,1,2] => 2
111100 => [4,2] => 1
111101 => [4,1,1] => 2
111110 => [5,1] => 1
111111 => [6] => 1
0000000 => [7] => 1
0000001 => [6,1] => 1
0000010 => [5,1,1] => 2
0000011 => [5,2] => 1
0000100 => [4,1,2] => 2
0000101 => [4,1,1,1] => 3
0000110 => [4,2,1] => 1
0000111 => [4,3] => 1
0001000 => [3,1,3] => 2
0001001 => [3,1,2,1] => 2
0001010 => [3,1,1,1,1] => 4
0001011 => [3,1,1,2] => 3
0001100 => [3,2,2] => 2
0001101 => [3,2,1,1] => 2
0001110 => [3,3,1] => 2
0001111 => [3,4] => 2
0010000 => [2,1,4] => 2
0010001 => [2,1,3,1] => 2
0010010 => [2,1,2,1,1] => 3
0010011 => [2,1,2,2] => 3
0010100 => [2,1,1,1,2] => 4
0010101 => [2,1,1,1,1,1] => 5
0010110 => [2,1,1,2,1] => 3
0010111 => [2,1,1,3] => 3
0011000 => [2,2,3] => 3
0011001 => [2,2,2,1] => 3
0011010 => [2,2,1,1,1] => 3
0011011 => [2,2,1,2] => 3
0011100 => [2,3,2] => 2
0011101 => [2,3,1,1] => 2
0011110 => [2,4,1] => 2
0011111 => [2,5] => 2
0100000 => [1,1,5] => 3
0100001 => [1,1,4,1] => 3
0100010 => [1,1,3,1,1] => 4
0100011 => [1,1,3,2] => 3
0100100 => [1,1,2,1,2] => 4
0100101 => [1,1,2,1,1,1] => 5
0100110 => [1,1,2,2,1] => 4
0100111 => [1,1,2,3] => 4
0101000 => [1,1,1,1,3] => 5
0101001 => [1,1,1,1,2,1] => 5
0101010 => [1,1,1,1,1,1,1] => 7
0101011 => [1,1,1,1,1,2] => 6
0101100 => [1,1,1,2,2] => 5
0101101 => [1,1,1,2,1,1] => 5
0101110 => [1,1,1,3,1] => 4
0101111 => [1,1,1,4] => 4
0110000 => [1,2,4] => 3
0110001 => [1,2,3,1] => 3
0110010 => [1,2,2,1,1] => 3
0110011 => [1,2,2,2] => 4
0110100 => [1,2,1,1,2] => 4
0110101 => [1,2,1,1,1,1] => 5
0110110 => [1,2,1,2,1] => 3
0110111 => [1,2,1,3] => 3
0111000 => [1,3,3] => 3
0111001 => [1,3,2,1] => 2
0111010 => [1,3,1,1,1] => 4
0111011 => [1,3,1,2] => 3
0111100 => [1,4,2] => 2
0111101 => [1,4,1,1] => 3
0111110 => [1,5,1] => 2
0111111 => [1,6] => 2
1000000 => [1,6] => 2
1000001 => [1,5,1] => 2
1000010 => [1,4,1,1] => 3
1000011 => [1,4,2] => 2
1000100 => [1,3,1,2] => 3
1000101 => [1,3,1,1,1] => 4
1000110 => [1,3,2,1] => 2
1000111 => [1,3,3] => 3
1001000 => [1,2,1,3] => 3
1001001 => [1,2,1,2,1] => 3
1001010 => [1,2,1,1,1,1] => 5
1001011 => [1,2,1,1,2] => 4
1001100 => [1,2,2,2] => 4
1001101 => [1,2,2,1,1] => 3
1001110 => [1,2,3,1] => 3
1001111 => [1,2,4] => 3
1010000 => [1,1,1,4] => 4
1010001 => [1,1,1,3,1] => 4
1010010 => [1,1,1,2,1,1] => 5
1010011 => [1,1,1,2,2] => 5
1010100 => [1,1,1,1,1,2] => 6
1010101 => [1,1,1,1,1,1,1] => 7
1010110 => [1,1,1,1,2,1] => 5
1010111 => [1,1,1,1,3] => 5
1011000 => [1,1,2,3] => 4
1011001 => [1,1,2,2,1] => 4
1011010 => [1,1,2,1,1,1] => 5
1011011 => [1,1,2,1,2] => 4
1011100 => [1,1,3,2] => 3
1011101 => [1,1,3,1,1] => 4
1011110 => [1,1,4,1] => 3
1011111 => [1,1,5] => 3
1100000 => [2,5] => 2
1100001 => [2,4,1] => 2
1100010 => [2,3,1,1] => 2
1100011 => [2,3,2] => 2
1100100 => [2,2,1,2] => 3
1100101 => [2,2,1,1,1] => 3
1100110 => [2,2,2,1] => 3
1100111 => [2,2,3] => 3
1101000 => [2,1,1,3] => 3
1101001 => [2,1,1,2,1] => 3
1101010 => [2,1,1,1,1,1] => 5
1101011 => [2,1,1,1,2] => 4
1101100 => [2,1,2,2] => 3
1101101 => [2,1,2,1,1] => 3
1101110 => [2,1,3,1] => 2
1101111 => [2,1,4] => 2
1110000 => [3,4] => 2
1110001 => [3,3,1] => 2
1110010 => [3,2,1,1] => 2
1110011 => [3,2,2] => 2
1110100 => [3,1,1,2] => 3
1110101 => [3,1,1,1,1] => 4
1110110 => [3,1,2,1] => 2
1110111 => [3,1,3] => 2
1111000 => [4,3] => 1
1111001 => [4,2,1] => 1
1111010 => [4,1,1,1] => 3
1111011 => [4,1,2] => 2
1111100 => [5,2] => 1
1111101 => [5,1,1] => 2
1111110 => [6,1] => 1
1111111 => [7] => 1
00000000 => [8] => 1
00000001 => [7,1] => 1
00000010 => [6,1,1] => 2
00000011 => [6,2] => 1
00000100 => [5,1,2] => 2
00000101 => [5,1,1,1] => 3
00000110 => [5,2,1] => 1
00000111 => [5,3] => 1
00001000 => [4,1,3] => 2
00001001 => [4,1,2,1] => 2
00001010 => [4,1,1,1,1] => 4
00001011 => [4,1,1,2] => 3
00001100 => [4,2,2] => 2
00001101 => [4,2,1,1] => 2
00001110 => [4,3,1] => 1
00001111 => [4,4] => 2
00010000 => [3,1,4] => 2
00010001 => [3,1,3,1] => 2
00010010 => [3,1,2,1,1] => 3
00010011 => [3,1,2,2] => 3
00010100 => [3,1,1,1,2] => 4
00010101 => [3,1,1,1,1,1] => 5
00010110 => [3,1,1,2,1] => 3
00010111 => [3,1,1,3] => 3
00011000 => [3,2,3] => 2
00011001 => [3,2,2,1] => 2
00011010 => [3,2,1,1,1] => 3
00011011 => [3,2,1,2] => 2
00011100 => [3,3,2] => 2
00011101 => [3,3,1,1] => 2
00011110 => [3,4,1] => 2
00011111 => [3,5] => 2
00100000 => [2,1,5] => 2
00100001 => [2,1,4,1] => 2
00100010 => [2,1,3,1,1] => 3
00100011 => [2,1,3,2] => 2
00100100 => [2,1,2,1,2] => 3
00100101 => [2,1,2,1,1,1] => 4
00100110 => [2,1,2,2,1] => 3
00100111 => [2,1,2,3] => 3
00101000 => [2,1,1,1,3] => 4
00101001 => [2,1,1,1,2,1] => 4
00101010 => [2,1,1,1,1,1,1] => 6
00101011 => [2,1,1,1,1,2] => 5
00101100 => [2,1,1,2,2] => 4
00101101 => [2,1,1,2,1,1] => 4
00101110 => [2,1,1,3,1] => 3
00101111 => [2,1,1,4] => 3
00110000 => [2,2,4] => 3
00110001 => [2,2,3,1] => 3
00110010 => [2,2,2,1,1] => 3
00110011 => [2,2,2,2] => 4
00110100 => [2,2,1,1,2] => 3
00110101 => [2,2,1,1,1,1] => 4
00110110 => [2,2,1,2,1] => 3
00110111 => [2,2,1,3] => 3
00111000 => [2,3,3] => 3
00111001 => [2,3,2,1] => 2
00111010 => [2,3,1,1,1] => 3
00111011 => [2,3,1,2] => 2
00111100 => [2,4,2] => 2
00111101 => [2,4,1,1] => 2
00111110 => [2,5,1] => 2
00111111 => [2,6] => 2
01000000 => [1,1,6] => 3
01000001 => [1,1,5,1] => 3
01000010 => [1,1,4,1,1] => 4
01000011 => [1,1,4,2] => 3
01000100 => [1,1,3,1,2] => 4
01000101 => [1,1,3,1,1,1] => 5
01000110 => [1,1,3,2,1] => 3
01000111 => [1,1,3,3] => 4
01001000 => [1,1,2,1,3] => 4
01001001 => [1,1,2,1,2,1] => 4
01001010 => [1,1,2,1,1,1,1] => 6
01001011 => [1,1,2,1,1,2] => 5
01001100 => [1,1,2,2,2] => 5
01001101 => [1,1,2,2,1,1] => 4
01001110 => [1,1,2,3,1] => 4
01001111 => [1,1,2,4] => 4
01010000 => [1,1,1,1,4] => 5
01010001 => [1,1,1,1,3,1] => 5
01010010 => [1,1,1,1,2,1,1] => 6
01010011 => [1,1,1,1,2,2] => 6
01010100 => [1,1,1,1,1,1,2] => 7
01010101 => [1,1,1,1,1,1,1,1] => 8
01010110 => [1,1,1,1,1,2,1] => 6
01010111 => [1,1,1,1,1,3] => 6
01011000 => [1,1,1,2,3] => 5
01011001 => [1,1,1,2,2,1] => 5
01011010 => [1,1,1,2,1,1,1] => 6
01011011 => [1,1,1,2,1,2] => 5
01011100 => [1,1,1,3,2] => 4
01011101 => [1,1,1,3,1,1] => 5
01011110 => [1,1,1,4,1] => 4
01011111 => [1,1,1,5] => 4
01100000 => [1,2,5] => 3
01100001 => [1,2,4,1] => 3
01100010 => [1,2,3,1,1] => 3
01100011 => [1,2,3,2] => 3
01100100 => [1,2,2,1,2] => 4
01100101 => [1,2,2,1,1,1] => 4
01100110 => [1,2,2,2,1] => 4
01100111 => [1,2,2,3] => 4
01101000 => [1,2,1,1,3] => 4
01101001 => [1,2,1,1,2,1] => 4
01101010 => [1,2,1,1,1,1,1] => 6
01101011 => [1,2,1,1,1,2] => 5
01101100 => [1,2,1,2,2] => 4
01101101 => [1,2,1,2,1,1] => 4
01101110 => [1,2,1,3,1] => 3
01101111 => [1,2,1,4] => 3
01110000 => [1,3,4] => 3
01110001 => [1,3,3,1] => 3
01110010 => [1,3,2,1,1] => 3
01110011 => [1,3,2,2] => 3
01110100 => [1,3,1,1,2] => 4
01110101 => [1,3,1,1,1,1] => 5
01110110 => [1,3,1,2,1] => 3
01110111 => [1,3,1,3] => 3
01111000 => [1,4,3] => 2
01111001 => [1,4,2,1] => 2
01111010 => [1,4,1,1,1] => 4
01111011 => [1,4,1,2] => 3
01111100 => [1,5,2] => 2
01111101 => [1,5,1,1] => 3
01111110 => [1,6,1] => 2
01111111 => [1,7] => 2
10000000 => [1,7] => 2
10000001 => [1,6,1] => 2
10000010 => [1,5,1,1] => 3
10000011 => [1,5,2] => 2
10000100 => [1,4,1,2] => 3
10000101 => [1,4,1,1,1] => 4
10000110 => [1,4,2,1] => 2
10000111 => [1,4,3] => 2
10001000 => [1,3,1,3] => 3
10001001 => [1,3,1,2,1] => 3
10001010 => [1,3,1,1,1,1] => 5
10001011 => [1,3,1,1,2] => 4
10001100 => [1,3,2,2] => 3
10001101 => [1,3,2,1,1] => 3
10001110 => [1,3,3,1] => 3
10001111 => [1,3,4] => 3
10010000 => [1,2,1,4] => 3
10010001 => [1,2,1,3,1] => 3
10010010 => [1,2,1,2,1,1] => 4
10010011 => [1,2,1,2,2] => 4
10010100 => [1,2,1,1,1,2] => 5
10010101 => [1,2,1,1,1,1,1] => 6
10010110 => [1,2,1,1,2,1] => 4
10010111 => [1,2,1,1,3] => 4
10011000 => [1,2,2,3] => 4
10011001 => [1,2,2,2,1] => 4
10011010 => [1,2,2,1,1,1] => 4
10011011 => [1,2,2,1,2] => 4
10011100 => [1,2,3,2] => 3
10011101 => [1,2,3,1,1] => 3
10011110 => [1,2,4,1] => 3
10011111 => [1,2,5] => 3
10100000 => [1,1,1,5] => 4
10100001 => [1,1,1,4,1] => 4
10100010 => [1,1,1,3,1,1] => 5
10100011 => [1,1,1,3,2] => 4
10100100 => [1,1,1,2,1,2] => 5
10100101 => [1,1,1,2,1,1,1] => 6
10100110 => [1,1,1,2,2,1] => 5
10100111 => [1,1,1,2,3] => 5
10101000 => [1,1,1,1,1,3] => 6
10101001 => [1,1,1,1,1,2,1] => 6
10101010 => [1,1,1,1,1,1,1,1] => 8
10101011 => [1,1,1,1,1,1,2] => 7
10101100 => [1,1,1,1,2,2] => 6
10101101 => [1,1,1,1,2,1,1] => 6
10101110 => [1,1,1,1,3,1] => 5
10101111 => [1,1,1,1,4] => 5
10110000 => [1,1,2,4] => 4
10110001 => [1,1,2,3,1] => 4
10110010 => [1,1,2,2,1,1] => 4
10110011 => [1,1,2,2,2] => 5
10110100 => [1,1,2,1,1,2] => 5
10110101 => [1,1,2,1,1,1,1] => 6
10110110 => [1,1,2,1,2,1] => 4
10110111 => [1,1,2,1,3] => 4
10111000 => [1,1,3,3] => 4
10111001 => [1,1,3,2,1] => 3
10111010 => [1,1,3,1,1,1] => 5
10111011 => [1,1,3,1,2] => 4
10111100 => [1,1,4,2] => 3
10111101 => [1,1,4,1,1] => 4
10111110 => [1,1,5,1] => 3
10111111 => [1,1,6] => 3
11000000 => [2,6] => 2
11000001 => [2,5,1] => 2
11000010 => [2,4,1,1] => 2
11000011 => [2,4,2] => 2
11000100 => [2,3,1,2] => 2
11000101 => [2,3,1,1,1] => 3
11000110 => [2,3,2,1] => 2
11000111 => [2,3,3] => 3
11001000 => [2,2,1,3] => 3
11001001 => [2,2,1,2,1] => 3
11001010 => [2,2,1,1,1,1] => 4
11001011 => [2,2,1,1,2] => 3
11001100 => [2,2,2,2] => 4
11001101 => [2,2,2,1,1] => 3
11001110 => [2,2,3,1] => 3
11001111 => [2,2,4] => 3
11010000 => [2,1,1,4] => 3
11010001 => [2,1,1,3,1] => 3
11010010 => [2,1,1,2,1,1] => 4
11010011 => [2,1,1,2,2] => 4
11010100 => [2,1,1,1,1,2] => 5
11010101 => [2,1,1,1,1,1,1] => 6
11010110 => [2,1,1,1,2,1] => 4
11010111 => [2,1,1,1,3] => 4
11011000 => [2,1,2,3] => 3
11011001 => [2,1,2,2,1] => 3
11011010 => [2,1,2,1,1,1] => 4
11011011 => [2,1,2,1,2] => 3
11011100 => [2,1,3,2] => 2
11011101 => [2,1,3,1,1] => 3
11011110 => [2,1,4,1] => 2
11011111 => [2,1,5] => 2
11100000 => [3,5] => 2
11100001 => [3,4,1] => 2
11100010 => [3,3,1,1] => 2
11100011 => [3,3,2] => 2
11100100 => [3,2,1,2] => 2
11100101 => [3,2,1,1,1] => 3
11100110 => [3,2,2,1] => 2
11100111 => [3,2,3] => 2
11101000 => [3,1,1,3] => 3
11101001 => [3,1,1,2,1] => 3
11101010 => [3,1,1,1,1,1] => 5
11101011 => [3,1,1,1,2] => 4
11101100 => [3,1,2,2] => 3
11101101 => [3,1,2,1,1] => 3
11101110 => [3,1,3,1] => 2
11101111 => [3,1,4] => 2
11110000 => [4,4] => 2
11110001 => [4,3,1] => 1
11110010 => [4,2,1,1] => 2
11110011 => [4,2,2] => 2
11110100 => [4,1,1,2] => 3
11110101 => [4,1,1,1,1] => 4
11110110 => [4,1,2,1] => 2
11110111 => [4,1,3] => 2
11111000 => [5,3] => 1
11111001 => [5,2,1] => 1
11111010 => [5,1,1,1] => 3
11111011 => [5,1,2] => 2
11111100 => [6,2] => 1
11111101 => [6,1,1] => 2
11111110 => [7,1] => 1
11111111 => [8] => 1
000000000 => [9] => 1
000000001 => [8,1] => 1
000000010 => [7,1,1] => 2
000000011 => [7,2] => 1
000000100 => [6,1,2] => 2
000000101 => [6,1,1,1] => 3
000000110 => [6,2,1] => 1
000000111 => [6,3] => 1
000001000 => [5,1,3] => 2
000001001 => [5,1,2,1] => 2
000001010 => [5,1,1,1,1] => 4
000001011 => [5,1,1,2] => 3
000001100 => [5,2,2] => 2
000001101 => [5,2,1,1] => 2
000001110 => [5,3,1] => 1
000001111 => [5,4] => 1
000010000 => [4,1,4] => 2
000010001 => [4,1,3,1] => 2
000010010 => [4,1,2,1,1] => 3
000010011 => [4,1,2,2] => 3
000010100 => [4,1,1,1,2] => 4
000010101 => [4,1,1,1,1,1] => 5
000010110 => [4,1,1,2,1] => 3
000010111 => [4,1,1,3] => 3
000011000 => [4,2,3] => 2
000011001 => [4,2,2,1] => 2
000011010 => [4,2,1,1,1] => 3
000011011 => [4,2,1,2] => 2
000011100 => [4,3,2] => 1
000011101 => [4,3,1,1] => 2
000011110 => [4,4,1] => 2
000011111 => [4,5] => 2
000100000 => [3,1,5] => 2
000100001 => [3,1,4,1] => 2
000100010 => [3,1,3,1,1] => 3
000100011 => [3,1,3,2] => 2
000100100 => [3,1,2,1,2] => 3
000100101 => [3,1,2,1,1,1] => 4
000100110 => [3,1,2,2,1] => 3
000100111 => [3,1,2,3] => 3
000101000 => [3,1,1,1,3] => 4
000101001 => [3,1,1,1,2,1] => 4
000101010 => [3,1,1,1,1,1,1] => 6
000101011 => [3,1,1,1,1,2] => 5
000101100 => [3,1,1,2,2] => 4
000101101 => [3,1,1,2,1,1] => 4
000101110 => [3,1,1,3,1] => 3
000101111 => [3,1,1,4] => 3
000110000 => [3,2,4] => 2
000110001 => [3,2,3,1] => 2
000110010 => [3,2,2,1,1] => 2
000110011 => [3,2,2,2] => 3
000110100 => [3,2,1,1,2] => 3
000110101 => [3,2,1,1,1,1] => 4
000110110 => [3,2,1,2,1] => 2
000110111 => [3,2,1,3] => 2
000111000 => [3,3,3] => 3
000111001 => [3,3,2,1] => 2
000111010 => [3,3,1,1,1] => 3
000111011 => [3,3,1,2] => 2
000111100 => [3,4,2] => 2
000111101 => [3,4,1,1] => 2
000111110 => [3,5,1] => 2
000111111 => [3,6] => 2
001000000 => [2,1,6] => 2
001000001 => [2,1,5,1] => 2
001000010 => [2,1,4,1,1] => 3
001000011 => [2,1,4,2] => 2
001000100 => [2,1,3,1,2] => 3
001000101 => [2,1,3,1,1,1] => 4
001000110 => [2,1,3,2,1] => 2
001000111 => [2,1,3,3] => 3
001001000 => [2,1,2,1,3] => 3
001001001 => [2,1,2,1,2,1] => 3
001001010 => [2,1,2,1,1,1,1] => 5
001001011 => [2,1,2,1,1,2] => 4
001001100 => [2,1,2,2,2] => 4
001001101 => [2,1,2,2,1,1] => 3
001001110 => [2,1,2,3,1] => 3
001001111 => [2,1,2,4] => 3
001010000 => [2,1,1,1,4] => 4
001010001 => [2,1,1,1,3,1] => 4
001010010 => [2,1,1,1,2,1,1] => 5
001010011 => [2,1,1,1,2,2] => 5
001010100 => [2,1,1,1,1,1,2] => 6
001010101 => [2,1,1,1,1,1,1,1] => 7
001010110 => [2,1,1,1,1,2,1] => 5
001010111 => [2,1,1,1,1,3] => 5
001011000 => [2,1,1,2,3] => 4
001011001 => [2,1,1,2,2,1] => 4
001011010 => [2,1,1,2,1,1,1] => 5
001011011 => [2,1,1,2,1,2] => 4
001011100 => [2,1,1,3,2] => 3
001011101 => [2,1,1,3,1,1] => 4
001011110 => [2,1,1,4,1] => 3
001011111 => [2,1,1,5] => 3
001100000 => [2,2,5] => 3
001100001 => [2,2,4,1] => 3
001100010 => [2,2,3,1,1] => 3
001100011 => [2,2,3,2] => 3
001100100 => [2,2,2,1,2] => 4
001100101 => [2,2,2,1,1,1] => 3
001100110 => [2,2,2,2,1] => 4
001100111 => [2,2,2,3] => 4
001101000 => [2,2,1,1,3] => 3
001101001 => [2,2,1,1,2,1] => 3
001101010 => [2,2,1,1,1,1,1] => 5
001101011 => [2,2,1,1,1,2] => 4
001101100 => [2,2,1,2,2] => 4
001101101 => [2,2,1,2,1,1] => 3
001101110 => [2,2,1,3,1] => 3
001101111 => [2,2,1,4] => 3
001110000 => [2,3,4] => 3
001110001 => [2,3,3,1] => 3
001110010 => [2,3,2,1,1] => 2
001110011 => [2,3,2,2] => 3
001110100 => [2,3,1,1,2] => 3
001110101 => [2,3,1,1,1,1] => 4
001110110 => [2,3,1,2,1] => 2
001110111 => [2,3,1,3] => 3
001111000 => [2,4,3] => 2
001111001 => [2,4,2,1] => 2
001111010 => [2,4,1,1,1] => 3
001111011 => [2,4,1,2] => 2
001111100 => [2,5,2] => 2
001111101 => [2,5,1,1] => 2
001111110 => [2,6,1] => 2
001111111 => [2,7] => 2
010000000 => [1,1,7] => 3
010000001 => [1,1,6,1] => 3
010000010 => [1,1,5,1,1] => 4
010000011 => [1,1,5,2] => 3
010000100 => [1,1,4,1,2] => 4
010000101 => [1,1,4,1,1,1] => 5
010000110 => [1,1,4,2,1] => 3
010000111 => [1,1,4,3] => 3
010001000 => [1,1,3,1,3] => 4
010001001 => [1,1,3,1,2,1] => 4
010001010 => [1,1,3,1,1,1,1] => 6
010001011 => [1,1,3,1,1,2] => 5
010001100 => [1,1,3,2,2] => 4
010001101 => [1,1,3,2,1,1] => 4
010001110 => [1,1,3,3,1] => 4
010001111 => [1,1,3,4] => 4
010010000 => [1,1,2,1,4] => 4
010010001 => [1,1,2,1,3,1] => 4
010010010 => [1,1,2,1,2,1,1] => 5
010010011 => [1,1,2,1,2,2] => 5
010010100 => [1,1,2,1,1,1,2] => 6
010010101 => [1,1,2,1,1,1,1,1] => 7
010010110 => [1,1,2,1,1,2,1] => 5
010010111 => [1,1,2,1,1,3] => 5
010011000 => [1,1,2,2,3] => 5
010011001 => [1,1,2,2,2,1] => 5
010011010 => [1,1,2,2,1,1,1] => 5
010011011 => [1,1,2,2,1,2] => 5
010011100 => [1,1,2,3,2] => 4
010011101 => [1,1,2,3,1,1] => 4
010011110 => [1,1,2,4,1] => 4
010011111 => [1,1,2,5] => 4
010100000 => [1,1,1,1,5] => 5
010100001 => [1,1,1,1,4,1] => 5
010100010 => [1,1,1,1,3,1,1] => 6
010100011 => [1,1,1,1,3,2] => 5
010100100 => [1,1,1,1,2,1,2] => 6
010100101 => [1,1,1,1,2,1,1,1] => 7
010100110 => [1,1,1,1,2,2,1] => 6
010100111 => [1,1,1,1,2,3] => 6
010101000 => [1,1,1,1,1,1,3] => 7
010101001 => [1,1,1,1,1,1,2,1] => 7
010101010 => [1,1,1,1,1,1,1,1,1] => 9
010101011 => [1,1,1,1,1,1,1,2] => 8
010101100 => [1,1,1,1,1,2,2] => 7
010101101 => [1,1,1,1,1,2,1,1] => 7
010101110 => [1,1,1,1,1,3,1] => 6
010101111 => [1,1,1,1,1,4] => 6
010110000 => [1,1,1,2,4] => 5
010110001 => [1,1,1,2,3,1] => 5
010110010 => [1,1,1,2,2,1,1] => 5
010110011 => [1,1,1,2,2,2] => 6
010110100 => [1,1,1,2,1,1,2] => 6
010110101 => [1,1,1,2,1,1,1,1] => 7
010110110 => [1,1,1,2,1,2,1] => 5
010110111 => [1,1,1,2,1,3] => 5
010111000 => [1,1,1,3,3] => 5
010111001 => [1,1,1,3,2,1] => 4
010111010 => [1,1,1,3,1,1,1] => 6
010111011 => [1,1,1,3,1,2] => 5
010111100 => [1,1,1,4,2] => 4
010111101 => [1,1,1,4,1,1] => 5
010111110 => [1,1,1,5,1] => 4
010111111 => [1,1,1,6] => 4
011000000 => [1,2,6] => 3
011000001 => [1,2,5,1] => 3
011000010 => [1,2,4,1,1] => 3
011000011 => [1,2,4,2] => 3
011000100 => [1,2,3,1,2] => 3
011000101 => [1,2,3,1,1,1] => 4
011000110 => [1,2,3,2,1] => 3
011000111 => [1,2,3,3] => 4
011001000 => [1,2,2,1,3] => 4
011001001 => [1,2,2,1,2,1] => 4
011001010 => [1,2,2,1,1,1,1] => 5
011001011 => [1,2,2,1,1,2] => 4
011001100 => [1,2,2,2,2] => 5
011001101 => [1,2,2,2,1,1] => 4
011001110 => [1,2,2,3,1] => 4
011001111 => [1,2,2,4] => 4
011010000 => [1,2,1,1,4] => 4
011010001 => [1,2,1,1,3,1] => 4
011010010 => [1,2,1,1,2,1,1] => 5
011010011 => [1,2,1,1,2,2] => 5
011010100 => [1,2,1,1,1,1,2] => 6
011010101 => [1,2,1,1,1,1,1,1] => 7
011010110 => [1,2,1,1,1,2,1] => 5
011010111 => [1,2,1,1,1,3] => 5
011011000 => [1,2,1,2,3] => 4
011011001 => [1,2,1,2,2,1] => 4
011011010 => [1,2,1,2,1,1,1] => 5
011011011 => [1,2,1,2,1,2] => 4
011011100 => [1,2,1,3,2] => 3
011011101 => [1,2,1,3,1,1] => 4
011011110 => [1,2,1,4,1] => 3
011011111 => [1,2,1,5] => 3
011100000 => [1,3,5] => 3
011100001 => [1,3,4,1] => 3
011100010 => [1,3,3,1,1] => 3
011100011 => [1,3,3,2] => 3
011100100 => [1,3,2,1,2] => 3
011100101 => [1,3,2,1,1,1] => 4
011100110 => [1,3,2,2,1] => 3
011100111 => [1,3,2,3] => 3
011101000 => [1,3,1,1,3] => 4
011101001 => [1,3,1,1,2,1] => 4
011101010 => [1,3,1,1,1,1,1] => 6
011101011 => [1,3,1,1,1,2] => 5
011101100 => [1,3,1,2,2] => 4
011101101 => [1,3,1,2,1,1] => 4
011101110 => [1,3,1,3,1] => 3
011101111 => [1,3,1,4] => 3
011110000 => [1,4,4] => 3
011110001 => [1,4,3,1] => 2
011110010 => [1,4,2,1,1] => 3
011110011 => [1,4,2,2] => 3
011110100 => [1,4,1,1,2] => 4
011110101 => [1,4,1,1,1,1] => 5
011110110 => [1,4,1,2,1] => 3
011110111 => [1,4,1,3] => 3
011111000 => [1,5,3] => 2
011111001 => [1,5,2,1] => 2
011111010 => [1,5,1,1,1] => 4
011111011 => [1,5,1,2] => 3
011111100 => [1,6,2] => 2
011111101 => [1,6,1,1] => 3
011111110 => [1,7,1] => 2
011111111 => [1,8] => 2
100000000 => [1,8] => 2
100000001 => [1,7,1] => 2
100000010 => [1,6,1,1] => 3
100000011 => [1,6,2] => 2
100000100 => [1,5,1,2] => 3
100000101 => [1,5,1,1,1] => 4
100000110 => [1,5,2,1] => 2
100000111 => [1,5,3] => 2
100001000 => [1,4,1,3] => 3
100001001 => [1,4,1,2,1] => 3
100001010 => [1,4,1,1,1,1] => 5
100001011 => [1,4,1,1,2] => 4
100001100 => [1,4,2,2] => 3
100001101 => [1,4,2,1,1] => 3
100001110 => [1,4,3,1] => 2
100001111 => [1,4,4] => 3
100010000 => [1,3,1,4] => 3
100010001 => [1,3,1,3,1] => 3
100010010 => [1,3,1,2,1,1] => 4
100010011 => [1,3,1,2,2] => 4
100010100 => [1,3,1,1,1,2] => 5
100010101 => [1,3,1,1,1,1,1] => 6
100010110 => [1,3,1,1,2,1] => 4
100010111 => [1,3,1,1,3] => 4
100011000 => [1,3,2,3] => 3
100011001 => [1,3,2,2,1] => 3
100011010 => [1,3,2,1,1,1] => 4
100011011 => [1,3,2,1,2] => 3
100011100 => [1,3,3,2] => 3
100011101 => [1,3,3,1,1] => 3
100011110 => [1,3,4,1] => 3
100011111 => [1,3,5] => 3
100100000 => [1,2,1,5] => 3
100100001 => [1,2,1,4,1] => 3
100100010 => [1,2,1,3,1,1] => 4
100100011 => [1,2,1,3,2] => 3
100100100 => [1,2,1,2,1,2] => 4
100100101 => [1,2,1,2,1,1,1] => 5
100100110 => [1,2,1,2,2,1] => 4
100100111 => [1,2,1,2,3] => 4
100101000 => [1,2,1,1,1,3] => 5
100101001 => [1,2,1,1,1,2,1] => 5
100101010 => [1,2,1,1,1,1,1,1] => 7
100101011 => [1,2,1,1,1,1,2] => 6
100101100 => [1,2,1,1,2,2] => 5
100101101 => [1,2,1,1,2,1,1] => 5
100101110 => [1,2,1,1,3,1] => 4
100101111 => [1,2,1,1,4] => 4
100110000 => [1,2,2,4] => 4
100110001 => [1,2,2,3,1] => 4
100110010 => [1,2,2,2,1,1] => 4
100110011 => [1,2,2,2,2] => 5
100110100 => [1,2,2,1,1,2] => 4
100110101 => [1,2,2,1,1,1,1] => 5
100110110 => [1,2,2,1,2,1] => 4
100110111 => [1,2,2,1,3] => 4
100111000 => [1,2,3,3] => 4
100111001 => [1,2,3,2,1] => 3
100111010 => [1,2,3,1,1,1] => 4
100111011 => [1,2,3,1,2] => 3
100111100 => [1,2,4,2] => 3
100111101 => [1,2,4,1,1] => 3
100111110 => [1,2,5,1] => 3
100111111 => [1,2,6] => 3
101000000 => [1,1,1,6] => 4
101000001 => [1,1,1,5,1] => 4
101000010 => [1,1,1,4,1,1] => 5
101000011 => [1,1,1,4,2] => 4
101000100 => [1,1,1,3,1,2] => 5
101000101 => [1,1,1,3,1,1,1] => 6
101000110 => [1,1,1,3,2,1] => 4
101000111 => [1,1,1,3,3] => 5
101001000 => [1,1,1,2,1,3] => 5
101001001 => [1,1,1,2,1,2,1] => 5
101001010 => [1,1,1,2,1,1,1,1] => 7
101001011 => [1,1,1,2,1,1,2] => 6
101001100 => [1,1,1,2,2,2] => 6
101001101 => [1,1,1,2,2,1,1] => 5
101001110 => [1,1,1,2,3,1] => 5
101001111 => [1,1,1,2,4] => 5
101010000 => [1,1,1,1,1,4] => 6
101010001 => [1,1,1,1,1,3,1] => 6
101010010 => [1,1,1,1,1,2,1,1] => 7
101010011 => [1,1,1,1,1,2,2] => 7
101010100 => [1,1,1,1,1,1,1,2] => 8
101010101 => [1,1,1,1,1,1,1,1,1] => 9
101010110 => [1,1,1,1,1,1,2,1] => 7
101010111 => [1,1,1,1,1,1,3] => 7
101011000 => [1,1,1,1,2,3] => 6
101011001 => [1,1,1,1,2,2,1] => 6
101011010 => [1,1,1,1,2,1,1,1] => 7
101011011 => [1,1,1,1,2,1,2] => 6
101011100 => [1,1,1,1,3,2] => 5
101011101 => [1,1,1,1,3,1,1] => 6
101011110 => [1,1,1,1,4,1] => 5
101011111 => [1,1,1,1,5] => 5
101100000 => [1,1,2,5] => 4
101100001 => [1,1,2,4,1] => 4
101100010 => [1,1,2,3,1,1] => 4
101100011 => [1,1,2,3,2] => 4
101100100 => [1,1,2,2,1,2] => 5
101100101 => [1,1,2,2,1,1,1] => 5
101100110 => [1,1,2,2,2,1] => 5
101100111 => [1,1,2,2,3] => 5
101101000 => [1,1,2,1,1,3] => 5
101101001 => [1,1,2,1,1,2,1] => 5
101101010 => [1,1,2,1,1,1,1,1] => 7
101101011 => [1,1,2,1,1,1,2] => 6
101101100 => [1,1,2,1,2,2] => 5
101101101 => [1,1,2,1,2,1,1] => 5
101101110 => [1,1,2,1,3,1] => 4
101101111 => [1,1,2,1,4] => 4
101110000 => [1,1,3,4] => 4
101110001 => [1,1,3,3,1] => 4
101110010 => [1,1,3,2,1,1] => 4
101110011 => [1,1,3,2,2] => 4
101110100 => [1,1,3,1,1,2] => 5
101110101 => [1,1,3,1,1,1,1] => 6
101110110 => [1,1,3,1,2,1] => 4
101110111 => [1,1,3,1,3] => 4
101111000 => [1,1,4,3] => 3
101111001 => [1,1,4,2,1] => 3
101111010 => [1,1,4,1,1,1] => 5
101111011 => [1,1,4,1,2] => 4
101111100 => [1,1,5,2] => 3
101111101 => [1,1,5,1,1] => 4
101111110 => [1,1,6,1] => 3
101111111 => [1,1,7] => 3
110000000 => [2,7] => 2
110000001 => [2,6,1] => 2
110000010 => [2,5,1,1] => 2
110000011 => [2,5,2] => 2
110000100 => [2,4,1,2] => 2
110000101 => [2,4,1,1,1] => 3
110000110 => [2,4,2,1] => 2
110000111 => [2,4,3] => 2
110001000 => [2,3,1,3] => 3
110001001 => [2,3,1,2,1] => 2
110001010 => [2,3,1,1,1,1] => 4
110001011 => [2,3,1,1,2] => 3
110001100 => [2,3,2,2] => 3
110001101 => [2,3,2,1,1] => 2
110001110 => [2,3,3,1] => 3
110001111 => [2,3,4] => 3
110010000 => [2,2,1,4] => 3
110010001 => [2,2,1,3,1] => 3
110010010 => [2,2,1,2,1,1] => 3
110010011 => [2,2,1,2,2] => 4
110010100 => [2,2,1,1,1,2] => 4
110010101 => [2,2,1,1,1,1,1] => 5
110010110 => [2,2,1,1,2,1] => 3
110010111 => [2,2,1,1,3] => 3
110011000 => [2,2,2,3] => 4
110011001 => [2,2,2,2,1] => 4
110011010 => [2,2,2,1,1,1] => 3
110011011 => [2,2,2,1,2] => 4
110011100 => [2,2,3,2] => 3
110011101 => [2,2,3,1,1] => 3
110011110 => [2,2,4,1] => 3
110011111 => [2,2,5] => 3
110100000 => [2,1,1,5] => 3
110100001 => [2,1,1,4,1] => 3
110100010 => [2,1,1,3,1,1] => 4
110100011 => [2,1,1,3,2] => 3
110100100 => [2,1,1,2,1,2] => 4
110100101 => [2,1,1,2,1,1,1] => 5
110100110 => [2,1,1,2,2,1] => 4
110100111 => [2,1,1,2,3] => 4
110101000 => [2,1,1,1,1,3] => 5
110101001 => [2,1,1,1,1,2,1] => 5
110101010 => [2,1,1,1,1,1,1,1] => 7
110101011 => [2,1,1,1,1,1,2] => 6
110101100 => [2,1,1,1,2,2] => 5
110101101 => [2,1,1,1,2,1,1] => 5
110101110 => [2,1,1,1,3,1] => 4
110101111 => [2,1,1,1,4] => 4
110110000 => [2,1,2,4] => 3
110110001 => [2,1,2,3,1] => 3
110110010 => [2,1,2,2,1,1] => 3
110110011 => [2,1,2,2,2] => 4
110110100 => [2,1,2,1,1,2] => 4
110110101 => [2,1,2,1,1,1,1] => 5
110110110 => [2,1,2,1,2,1] => 3
110110111 => [2,1,2,1,3] => 3
110111000 => [2,1,3,3] => 3
110111001 => [2,1,3,2,1] => 2
110111010 => [2,1,3,1,1,1] => 4
110111011 => [2,1,3,1,2] => 3
110111100 => [2,1,4,2] => 2
110111101 => [2,1,4,1,1] => 3
110111110 => [2,1,5,1] => 2
110111111 => [2,1,6] => 2
111000000 => [3,6] => 2
111000001 => [3,5,1] => 2
111000010 => [3,4,1,1] => 2
111000011 => [3,4,2] => 2
111000100 => [3,3,1,2] => 2
111000101 => [3,3,1,1,1] => 3
111000110 => [3,3,2,1] => 2
111000111 => [3,3,3] => 3
111001000 => [3,2,1,3] => 2
111001001 => [3,2,1,2,1] => 2
111001010 => [3,2,1,1,1,1] => 4
111001011 => [3,2,1,1,2] => 3
111001100 => [3,2,2,2] => 3
111001101 => [3,2,2,1,1] => 2
111001110 => [3,2,3,1] => 2
111001111 => [3,2,4] => 2
111010000 => [3,1,1,4] => 3
111010001 => [3,1,1,3,1] => 3
111010010 => [3,1,1,2,1,1] => 4
111010011 => [3,1,1,2,2] => 4
111010100 => [3,1,1,1,1,2] => 5
111010101 => [3,1,1,1,1,1,1] => 6
111010110 => [3,1,1,1,2,1] => 4
111010111 => [3,1,1,1,3] => 4
111011000 => [3,1,2,3] => 3
111011001 => [3,1,2,2,1] => 3
111011010 => [3,1,2,1,1,1] => 4
111011011 => [3,1,2,1,2] => 3
111011100 => [3,1,3,2] => 2
111011101 => [3,1,3,1,1] => 3
111011110 => [3,1,4,1] => 2
111011111 => [3,1,5] => 2
111100000 => [4,5] => 2
111100001 => [4,4,1] => 2
111100010 => [4,3,1,1] => 2
111100011 => [4,3,2] => 1
111100100 => [4,2,1,2] => 2
111100101 => [4,2,1,1,1] => 3
111100110 => [4,2,2,1] => 2
111100111 => [4,2,3] => 2
111101000 => [4,1,1,3] => 3
111101001 => [4,1,1,2,1] => 3
111101010 => [4,1,1,1,1,1] => 5
111101011 => [4,1,1,1,2] => 4
111101100 => [4,1,2,2] => 3
111101101 => [4,1,2,1,1] => 3
111101110 => [4,1,3,1] => 2
111101111 => [4,1,4] => 2
111110000 => [5,4] => 1
111110001 => [5,3,1] => 1
111110010 => [5,2,1,1] => 2
111110011 => [5,2,2] => 2
111110100 => [5,1,1,2] => 3
111110101 => [5,1,1,1,1] => 4
111110110 => [5,1,2,1] => 2
111110111 => [5,1,3] => 2
111111000 => [6,3] => 1
111111001 => [6,2,1] => 1
111111010 => [6,1,1,1] => 3
111111011 => [6,1,2] => 2
111111100 => [7,2] => 1
111111101 => [7,1,1] => 2
111111110 => [8,1] => 1
111111111 => [9] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,2 4,2,2 4,8,2,2 6,12,10,2,2 8,22,18,12,2,2 10,36,42,22,14,2,2 12,60,78,60,26,16,2,2 16,94,148,124,78,30,18,2,2
$F_{1} = 2\ q$
$F_{2} = 2\ q + 2\ q^{2}$
$F_{3} = 4\ q + 2\ q^{2} + 2\ q^{3}$
$F_{4} = 4\ q + 8\ q^{2} + 2\ q^{3} + 2\ q^{4}$
$F_{5} = 6\ q + 12\ q^{2} + 10\ q^{3} + 2\ q^{4} + 2\ q^{5}$
$F_{6} = 8\ q + 22\ q^{2} + 18\ q^{3} + 12\ q^{4} + 2\ q^{5} + 2\ q^{6}$
$F_{7} = 10\ q + 36\ q^{2} + 42\ q^{3} + 22\ q^{4} + 14\ q^{5} + 2\ q^{6} + 2\ q^{7}$
$F_{8} = 12\ q + 60\ q^{2} + 78\ q^{3} + 60\ q^{4} + 26\ q^{5} + 16\ q^{6} + 2\ q^{7} + 2\ q^{8}$
$F_{9} = 16\ q + 94\ q^{2} + 148\ q^{3} + 124\ q^{4} + 78\ q^{5} + 30\ q^{6} + 18\ q^{7} + 2\ q^{8} + 2\ q^{9}$
Description
The length of the longest weakly inreasing subsequence of parts of an integer composition.
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 $w$.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
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