Identifier
-
Mp00097:
Binary words
—delta morphism⟶
Integer compositions
St000761: Integer compositions ⟶ ℤ
Values
0 => [1] => 0
1 => [1] => 0
00 => [2] => 0
01 => [1,1] => 0
10 => [1,1] => 0
11 => [2] => 0
000 => [3] => 0
001 => [2,1] => 0
010 => [1,1,1] => 0
011 => [1,2] => 1
100 => [1,2] => 1
101 => [1,1,1] => 0
110 => [2,1] => 0
111 => [3] => 0
0000 => [4] => 0
0001 => [3,1] => 0
0010 => [2,1,1] => 0
0011 => [2,2] => 0
0100 => [1,1,2] => 1
0101 => [1,1,1,1] => 0
0110 => [1,2,1] => 1
0111 => [1,3] => 1
1000 => [1,3] => 1
1001 => [1,2,1] => 1
1010 => [1,1,1,1] => 0
1011 => [1,1,2] => 1
1100 => [2,2] => 0
1101 => [2,1,1] => 0
1110 => [3,1] => 0
1111 => [4] => 0
00000 => [5] => 0
00001 => [4,1] => 0
00010 => [3,1,1] => 0
00011 => [3,2] => 0
00100 => [2,1,2] => 1
00101 => [2,1,1,1] => 0
00110 => [2,2,1] => 0
00111 => [2,3] => 1
01000 => [1,1,3] => 1
01001 => [1,1,2,1] => 1
01010 => [1,1,1,1,1] => 0
01011 => [1,1,1,2] => 1
01100 => [1,2,2] => 1
01101 => [1,2,1,1] => 1
01110 => [1,3,1] => 1
01111 => [1,4] => 1
10000 => [1,4] => 1
10001 => [1,3,1] => 1
10010 => [1,2,1,1] => 1
10011 => [1,2,2] => 1
10100 => [1,1,1,2] => 1
10101 => [1,1,1,1,1] => 0
10110 => [1,1,2,1] => 1
10111 => [1,1,3] => 1
11000 => [2,3] => 1
11001 => [2,2,1] => 0
11010 => [2,1,1,1] => 0
11011 => [2,1,2] => 1
11100 => [3,2] => 0
11101 => [3,1,1] => 0
11110 => [4,1] => 0
11111 => [5] => 0
000000 => [6] => 0
000001 => [5,1] => 0
000010 => [4,1,1] => 0
000011 => [4,2] => 0
000100 => [3,1,2] => 1
000101 => [3,1,1,1] => 0
000110 => [3,2,1] => 0
000111 => [3,3] => 0
001000 => [2,1,3] => 1
001001 => [2,1,2,1] => 1
001010 => [2,1,1,1,1] => 0
001011 => [2,1,1,2] => 1
001100 => [2,2,2] => 0
001101 => [2,2,1,1] => 0
001110 => [2,3,1] => 1
001111 => [2,4] => 1
010000 => [1,1,4] => 1
010001 => [1,1,3,1] => 1
010010 => [1,1,2,1,1] => 1
010011 => [1,1,2,2] => 1
010100 => [1,1,1,1,2] => 1
010101 => [1,1,1,1,1,1] => 0
010110 => [1,1,1,2,1] => 1
010111 => [1,1,1,3] => 1
011000 => [1,2,3] => 2
011001 => [1,2,2,1] => 1
011010 => [1,2,1,1,1] => 1
011011 => [1,2,1,2] => 2
011100 => [1,3,2] => 1
011101 => [1,3,1,1] => 1
011110 => [1,4,1] => 1
011111 => [1,5] => 1
100000 => [1,5] => 1
100001 => [1,4,1] => 1
100010 => [1,3,1,1] => 1
100011 => [1,3,2] => 1
100100 => [1,2,1,2] => 2
100101 => [1,2,1,1,1] => 1
100110 => [1,2,2,1] => 1
>>> Load all 1022 entries. <<<100111 => [1,2,3] => 2
101000 => [1,1,1,3] => 1
101001 => [1,1,1,2,1] => 1
101010 => [1,1,1,1,1,1] => 0
101011 => [1,1,1,1,2] => 1
101100 => [1,1,2,2] => 1
101101 => [1,1,2,1,1] => 1
101110 => [1,1,3,1] => 1
101111 => [1,1,4] => 1
110000 => [2,4] => 1
110001 => [2,3,1] => 1
110010 => [2,2,1,1] => 0
110011 => [2,2,2] => 0
110100 => [2,1,1,2] => 1
110101 => [2,1,1,1,1] => 0
110110 => [2,1,2,1] => 1
110111 => [2,1,3] => 1
111000 => [3,3] => 0
111001 => [3,2,1] => 0
111010 => [3,1,1,1] => 0
111011 => [3,1,2] => 1
111100 => [4,2] => 0
111101 => [4,1,1] => 0
111110 => [5,1] => 0
111111 => [6] => 0
0000000 => [7] => 0
0000001 => [6,1] => 0
0000010 => [5,1,1] => 0
0000011 => [5,2] => 0
0000100 => [4,1,2] => 1
0000101 => [4,1,1,1] => 0
0000110 => [4,2,1] => 0
0000111 => [4,3] => 0
0001000 => [3,1,3] => 1
0001001 => [3,1,2,1] => 1
0001010 => [3,1,1,1,1] => 0
0001011 => [3,1,1,2] => 1
0001100 => [3,2,2] => 0
0001101 => [3,2,1,1] => 0
0001110 => [3,3,1] => 0
0001111 => [3,4] => 1
0010000 => [2,1,4] => 1
0010001 => [2,1,3,1] => 1
0010010 => [2,1,2,1,1] => 1
0010011 => [2,1,2,2] => 1
0010100 => [2,1,1,1,2] => 1
0010101 => [2,1,1,1,1,1] => 0
0010110 => [2,1,1,2,1] => 1
0010111 => [2,1,1,3] => 1
0011000 => [2,2,3] => 1
0011001 => [2,2,2,1] => 0
0011010 => [2,2,1,1,1] => 0
0011011 => [2,2,1,2] => 1
0011100 => [2,3,2] => 1
0011101 => [2,3,1,1] => 1
0011110 => [2,4,1] => 1
0011111 => [2,5] => 1
0100000 => [1,1,5] => 1
0100001 => [1,1,4,1] => 1
0100010 => [1,1,3,1,1] => 1
0100011 => [1,1,3,2] => 1
0100100 => [1,1,2,1,2] => 2
0100101 => [1,1,2,1,1,1] => 1
0100110 => [1,1,2,2,1] => 1
0100111 => [1,1,2,3] => 2
0101000 => [1,1,1,1,3] => 1
0101001 => [1,1,1,1,2,1] => 1
0101010 => [1,1,1,1,1,1,1] => 0
0101011 => [1,1,1,1,1,2] => 1
0101100 => [1,1,1,2,2] => 1
0101101 => [1,1,1,2,1,1] => 1
0101110 => [1,1,1,3,1] => 1
0101111 => [1,1,1,4] => 1
0110000 => [1,2,4] => 2
0110001 => [1,2,3,1] => 2
0110010 => [1,2,2,1,1] => 1
0110011 => [1,2,2,2] => 1
0110100 => [1,2,1,1,2] => 2
0110101 => [1,2,1,1,1,1] => 1
0110110 => [1,2,1,2,1] => 2
0110111 => [1,2,1,3] => 2
0111000 => [1,3,3] => 1
0111001 => [1,3,2,1] => 1
0111010 => [1,3,1,1,1] => 1
0111011 => [1,3,1,2] => 2
0111100 => [1,4,2] => 1
0111101 => [1,4,1,1] => 1
0111110 => [1,5,1] => 1
0111111 => [1,6] => 1
1000000 => [1,6] => 1
1000001 => [1,5,1] => 1
1000010 => [1,4,1,1] => 1
1000011 => [1,4,2] => 1
1000100 => [1,3,1,2] => 2
1000101 => [1,3,1,1,1] => 1
1000110 => [1,3,2,1] => 1
1000111 => [1,3,3] => 1
1001000 => [1,2,1,3] => 2
1001001 => [1,2,1,2,1] => 2
1001010 => [1,2,1,1,1,1] => 1
1001011 => [1,2,1,1,2] => 2
1001100 => [1,2,2,2] => 1
1001101 => [1,2,2,1,1] => 1
1001110 => [1,2,3,1] => 2
1001111 => [1,2,4] => 2
1010000 => [1,1,1,4] => 1
1010001 => [1,1,1,3,1] => 1
1010010 => [1,1,1,2,1,1] => 1
1010011 => [1,1,1,2,2] => 1
1010100 => [1,1,1,1,1,2] => 1
1010101 => [1,1,1,1,1,1,1] => 0
1010110 => [1,1,1,1,2,1] => 1
1010111 => [1,1,1,1,3] => 1
1011000 => [1,1,2,3] => 2
1011001 => [1,1,2,2,1] => 1
1011010 => [1,1,2,1,1,1] => 1
1011011 => [1,1,2,1,2] => 2
1011100 => [1,1,3,2] => 1
1011101 => [1,1,3,1,1] => 1
1011110 => [1,1,4,1] => 1
1011111 => [1,1,5] => 1
1100000 => [2,5] => 1
1100001 => [2,4,1] => 1
1100010 => [2,3,1,1] => 1
1100011 => [2,3,2] => 1
1100100 => [2,2,1,2] => 1
1100101 => [2,2,1,1,1] => 0
1100110 => [2,2,2,1] => 0
1100111 => [2,2,3] => 1
1101000 => [2,1,1,3] => 1
1101001 => [2,1,1,2,1] => 1
1101010 => [2,1,1,1,1,1] => 0
1101011 => [2,1,1,1,2] => 1
1101100 => [2,1,2,2] => 1
1101101 => [2,1,2,1,1] => 1
1101110 => [2,1,3,1] => 1
1101111 => [2,1,4] => 1
1110000 => [3,4] => 1
1110001 => [3,3,1] => 0
1110010 => [3,2,1,1] => 0
1110011 => [3,2,2] => 0
1110100 => [3,1,1,2] => 1
1110101 => [3,1,1,1,1] => 0
1110110 => [3,1,2,1] => 1
1110111 => [3,1,3] => 1
1111000 => [4,3] => 0
1111001 => [4,2,1] => 0
1111010 => [4,1,1,1] => 0
1111011 => [4,1,2] => 1
1111100 => [5,2] => 0
1111101 => [5,1,1] => 0
1111110 => [6,1] => 0
1111111 => [7] => 0
00000000 => [8] => 0
00000001 => [7,1] => 0
00000010 => [6,1,1] => 0
00000011 => [6,2] => 0
00000100 => [5,1,2] => 1
00000101 => [5,1,1,1] => 0
00000110 => [5,2,1] => 0
00000111 => [5,3] => 0
00001000 => [4,1,3] => 1
00001001 => [4,1,2,1] => 1
00001010 => [4,1,1,1,1] => 0
00001011 => [4,1,1,2] => 1
00001100 => [4,2,2] => 0
00001101 => [4,2,1,1] => 0
00001110 => [4,3,1] => 0
00001111 => [4,4] => 0
00010000 => [3,1,4] => 1
00010001 => [3,1,3,1] => 1
00010010 => [3,1,2,1,1] => 1
00010011 => [3,1,2,2] => 1
00010100 => [3,1,1,1,2] => 1
00010101 => [3,1,1,1,1,1] => 0
00010110 => [3,1,1,2,1] => 1
00010111 => [3,1,1,3] => 1
00011000 => [3,2,3] => 1
00011001 => [3,2,2,1] => 0
00011010 => [3,2,1,1,1] => 0
00011011 => [3,2,1,2] => 1
00011100 => [3,3,2] => 0
00011101 => [3,3,1,1] => 0
00011110 => [3,4,1] => 1
00011111 => [3,5] => 1
00100000 => [2,1,5] => 1
00100001 => [2,1,4,1] => 1
00100010 => [2,1,3,1,1] => 1
00100011 => [2,1,3,2] => 1
00100100 => [2,1,2,1,2] => 2
00100101 => [2,1,2,1,1,1] => 1
00100110 => [2,1,2,2,1] => 1
00100111 => [2,1,2,3] => 2
00101000 => [2,1,1,1,3] => 1
00101001 => [2,1,1,1,2,1] => 1
00101010 => [2,1,1,1,1,1,1] => 0
00101011 => [2,1,1,1,1,2] => 1
00101100 => [2,1,1,2,2] => 1
00101101 => [2,1,1,2,1,1] => 1
00101110 => [2,1,1,3,1] => 1
00101111 => [2,1,1,4] => 1
00110000 => [2,2,4] => 1
00110001 => [2,2,3,1] => 1
00110010 => [2,2,2,1,1] => 0
00110011 => [2,2,2,2] => 0
00110100 => [2,2,1,1,2] => 1
00110101 => [2,2,1,1,1,1] => 0
00110110 => [2,2,1,2,1] => 1
00110111 => [2,2,1,3] => 1
00111000 => [2,3,3] => 1
00111001 => [2,3,2,1] => 1
00111010 => [2,3,1,1,1] => 1
00111011 => [2,3,1,2] => 2
00111100 => [2,4,2] => 1
00111101 => [2,4,1,1] => 1
00111110 => [2,5,1] => 1
00111111 => [2,6] => 1
01000000 => [1,1,6] => 1
01000001 => [1,1,5,1] => 1
01000010 => [1,1,4,1,1] => 1
01000011 => [1,1,4,2] => 1
01000100 => [1,1,3,1,2] => 2
01000101 => [1,1,3,1,1,1] => 1
01000110 => [1,1,3,2,1] => 1
01000111 => [1,1,3,3] => 1
01001000 => [1,1,2,1,3] => 2
01001001 => [1,1,2,1,2,1] => 2
01001010 => [1,1,2,1,1,1,1] => 1
01001011 => [1,1,2,1,1,2] => 2
01001100 => [1,1,2,2,2] => 1
01001101 => [1,1,2,2,1,1] => 1
01001110 => [1,1,2,3,1] => 2
01001111 => [1,1,2,4] => 2
01010000 => [1,1,1,1,4] => 1
01010001 => [1,1,1,1,3,1] => 1
01010010 => [1,1,1,1,2,1,1] => 1
01010011 => [1,1,1,1,2,2] => 1
01010100 => [1,1,1,1,1,1,2] => 1
01010101 => [1,1,1,1,1,1,1,1] => 0
01010110 => [1,1,1,1,1,2,1] => 1
01010111 => [1,1,1,1,1,3] => 1
01011000 => [1,1,1,2,3] => 2
01011001 => [1,1,1,2,2,1] => 1
01011010 => [1,1,1,2,1,1,1] => 1
01011011 => [1,1,1,2,1,2] => 2
01011100 => [1,1,1,3,2] => 1
01011101 => [1,1,1,3,1,1] => 1
01011110 => [1,1,1,4,1] => 1
01011111 => [1,1,1,5] => 1
01100000 => [1,2,5] => 2
01100001 => [1,2,4,1] => 2
01100010 => [1,2,3,1,1] => 2
01100011 => [1,2,3,2] => 2
01100100 => [1,2,2,1,2] => 2
01100101 => [1,2,2,1,1,1] => 1
01100110 => [1,2,2,2,1] => 1
01100111 => [1,2,2,3] => 2
01101000 => [1,2,1,1,3] => 2
01101001 => [1,2,1,1,2,1] => 2
01101010 => [1,2,1,1,1,1,1] => 1
01101011 => [1,2,1,1,1,2] => 2
01101100 => [1,2,1,2,2] => 2
01101101 => [1,2,1,2,1,1] => 2
01101110 => [1,2,1,3,1] => 2
01101111 => [1,2,1,4] => 2
01110000 => [1,3,4] => 2
01110001 => [1,3,3,1] => 1
01110010 => [1,3,2,1,1] => 1
01110011 => [1,3,2,2] => 1
01110100 => [1,3,1,1,2] => 2
01110101 => [1,3,1,1,1,1] => 1
01110110 => [1,3,1,2,1] => 2
01110111 => [1,3,1,3] => 2
01111000 => [1,4,3] => 1
01111001 => [1,4,2,1] => 1
01111010 => [1,4,1,1,1] => 1
01111011 => [1,4,1,2] => 2
01111100 => [1,5,2] => 1
01111101 => [1,5,1,1] => 1
01111110 => [1,6,1] => 1
01111111 => [1,7] => 1
10000000 => [1,7] => 1
10000001 => [1,6,1] => 1
10000010 => [1,5,1,1] => 1
10000011 => [1,5,2] => 1
10000100 => [1,4,1,2] => 2
10000101 => [1,4,1,1,1] => 1
10000110 => [1,4,2,1] => 1
10000111 => [1,4,3] => 1
10001000 => [1,3,1,3] => 2
10001001 => [1,3,1,2,1] => 2
10001010 => [1,3,1,1,1,1] => 1
10001011 => [1,3,1,1,2] => 2
10001100 => [1,3,2,2] => 1
10001101 => [1,3,2,1,1] => 1
10001110 => [1,3,3,1] => 1
10001111 => [1,3,4] => 2
10010000 => [1,2,1,4] => 2
10010001 => [1,2,1,3,1] => 2
10010010 => [1,2,1,2,1,1] => 2
10010011 => [1,2,1,2,2] => 2
10010100 => [1,2,1,1,1,2] => 2
10010101 => [1,2,1,1,1,1,1] => 1
10010110 => [1,2,1,1,2,1] => 2
10010111 => [1,2,1,1,3] => 2
10011000 => [1,2,2,3] => 2
10011001 => [1,2,2,2,1] => 1
10011010 => [1,2,2,1,1,1] => 1
10011011 => [1,2,2,1,2] => 2
10011100 => [1,2,3,2] => 2
10011101 => [1,2,3,1,1] => 2
10011110 => [1,2,4,1] => 2
10011111 => [1,2,5] => 2
10100000 => [1,1,1,5] => 1
10100001 => [1,1,1,4,1] => 1
10100010 => [1,1,1,3,1,1] => 1
10100011 => [1,1,1,3,2] => 1
10100100 => [1,1,1,2,1,2] => 2
10100101 => [1,1,1,2,1,1,1] => 1
10100110 => [1,1,1,2,2,1] => 1
10100111 => [1,1,1,2,3] => 2
10101000 => [1,1,1,1,1,3] => 1
10101001 => [1,1,1,1,1,2,1] => 1
10101010 => [1,1,1,1,1,1,1,1] => 0
10101011 => [1,1,1,1,1,1,2] => 1
10101100 => [1,1,1,1,2,2] => 1
10101101 => [1,1,1,1,2,1,1] => 1
10101110 => [1,1,1,1,3,1] => 1
10101111 => [1,1,1,1,4] => 1
10110000 => [1,1,2,4] => 2
10110001 => [1,1,2,3,1] => 2
10110010 => [1,1,2,2,1,1] => 1
10110011 => [1,1,2,2,2] => 1
10110100 => [1,1,2,1,1,2] => 2
10110101 => [1,1,2,1,1,1,1] => 1
10110110 => [1,1,2,1,2,1] => 2
10110111 => [1,1,2,1,3] => 2
10111000 => [1,1,3,3] => 1
10111001 => [1,1,3,2,1] => 1
10111010 => [1,1,3,1,1,1] => 1
10111011 => [1,1,3,1,2] => 2
10111100 => [1,1,4,2] => 1
10111101 => [1,1,4,1,1] => 1
10111110 => [1,1,5,1] => 1
10111111 => [1,1,6] => 1
11000000 => [2,6] => 1
11000001 => [2,5,1] => 1
11000010 => [2,4,1,1] => 1
11000011 => [2,4,2] => 1
11000100 => [2,3,1,2] => 2
11000101 => [2,3,1,1,1] => 1
11000110 => [2,3,2,1] => 1
11000111 => [2,3,3] => 1
11001000 => [2,2,1,3] => 1
11001001 => [2,2,1,2,1] => 1
11001010 => [2,2,1,1,1,1] => 0
11001011 => [2,2,1,1,2] => 1
11001100 => [2,2,2,2] => 0
11001101 => [2,2,2,1,1] => 0
11001110 => [2,2,3,1] => 1
11001111 => [2,2,4] => 1
11010000 => [2,1,1,4] => 1
11010001 => [2,1,1,3,1] => 1
11010010 => [2,1,1,2,1,1] => 1
11010011 => [2,1,1,2,2] => 1
11010100 => [2,1,1,1,1,2] => 1
11010101 => [2,1,1,1,1,1,1] => 0
11010110 => [2,1,1,1,2,1] => 1
11010111 => [2,1,1,1,3] => 1
11011000 => [2,1,2,3] => 2
11011001 => [2,1,2,2,1] => 1
11011010 => [2,1,2,1,1,1] => 1
11011011 => [2,1,2,1,2] => 2
11011100 => [2,1,3,2] => 1
11011101 => [2,1,3,1,1] => 1
11011110 => [2,1,4,1] => 1
11011111 => [2,1,5] => 1
11100000 => [3,5] => 1
11100001 => [3,4,1] => 1
11100010 => [3,3,1,1] => 0
11100011 => [3,3,2] => 0
11100100 => [3,2,1,2] => 1
11100101 => [3,2,1,1,1] => 0
11100110 => [3,2,2,1] => 0
11100111 => [3,2,3] => 1
11101000 => [3,1,1,3] => 1
11101001 => [3,1,1,2,1] => 1
11101010 => [3,1,1,1,1,1] => 0
11101011 => [3,1,1,1,2] => 1
11101100 => [3,1,2,2] => 1
11101101 => [3,1,2,1,1] => 1
11101110 => [3,1,3,1] => 1
11101111 => [3,1,4] => 1
11110000 => [4,4] => 0
11110001 => [4,3,1] => 0
11110010 => [4,2,1,1] => 0
11110011 => [4,2,2] => 0
11110100 => [4,1,1,2] => 1
11110101 => [4,1,1,1,1] => 0
11110110 => [4,1,2,1] => 1
11110111 => [4,1,3] => 1
11111000 => [5,3] => 0
11111001 => [5,2,1] => 0
11111010 => [5,1,1,1] => 0
11111011 => [5,1,2] => 1
11111100 => [6,2] => 0
11111101 => [6,1,1] => 0
11111110 => [7,1] => 0
11111111 => [8] => 0
000000000 => [9] => 0
000000001 => [8,1] => 0
000000010 => [7,1,1] => 0
000000011 => [7,2] => 0
000000100 => [6,1,2] => 1
000000101 => [6,1,1,1] => 0
000000110 => [6,2,1] => 0
000000111 => [6,3] => 0
000001000 => [5,1,3] => 1
000001001 => [5,1,2,1] => 1
000001010 => [5,1,1,1,1] => 0
000001011 => [5,1,1,2] => 1
000001100 => [5,2,2] => 0
000001101 => [5,2,1,1] => 0
000001110 => [5,3,1] => 0
000001111 => [5,4] => 0
000010000 => [4,1,4] => 1
000010001 => [4,1,3,1] => 1
000010010 => [4,1,2,1,1] => 1
000010011 => [4,1,2,2] => 1
000010100 => [4,1,1,1,2] => 1
000010101 => [4,1,1,1,1,1] => 0
000010110 => [4,1,1,2,1] => 1
000010111 => [4,1,1,3] => 1
000011000 => [4,2,3] => 1
000011001 => [4,2,2,1] => 0
000011010 => [4,2,1,1,1] => 0
000011011 => [4,2,1,2] => 1
000011100 => [4,3,2] => 0
000011101 => [4,3,1,1] => 0
000011110 => [4,4,1] => 0
000011111 => [4,5] => 1
000100000 => [3,1,5] => 1
000100001 => [3,1,4,1] => 1
000100010 => [3,1,3,1,1] => 1
000100011 => [3,1,3,2] => 1
000100100 => [3,1,2,1,2] => 2
000100101 => [3,1,2,1,1,1] => 1
000100110 => [3,1,2,2,1] => 1
000100111 => [3,1,2,3] => 2
000101000 => [3,1,1,1,3] => 1
000101001 => [3,1,1,1,2,1] => 1
000101010 => [3,1,1,1,1,1,1] => 0
000101011 => [3,1,1,1,1,2] => 1
000101100 => [3,1,1,2,2] => 1
000101101 => [3,1,1,2,1,1] => 1
000101110 => [3,1,1,3,1] => 1
000101111 => [3,1,1,4] => 1
000110000 => [3,2,4] => 1
000110001 => [3,2,3,1] => 1
000110010 => [3,2,2,1,1] => 0
000110011 => [3,2,2,2] => 0
000110100 => [3,2,1,1,2] => 1
000110101 => [3,2,1,1,1,1] => 0
000110110 => [3,2,1,2,1] => 1
000110111 => [3,2,1,3] => 1
000111000 => [3,3,3] => 0
000111001 => [3,3,2,1] => 0
000111010 => [3,3,1,1,1] => 0
000111011 => [3,3,1,2] => 1
000111100 => [3,4,2] => 1
000111101 => [3,4,1,1] => 1
000111110 => [3,5,1] => 1
000111111 => [3,6] => 1
001000000 => [2,1,6] => 1
001000001 => [2,1,5,1] => 1
001000010 => [2,1,4,1,1] => 1
001000011 => [2,1,4,2] => 1
001000100 => [2,1,3,1,2] => 2
001000101 => [2,1,3,1,1,1] => 1
001000110 => [2,1,3,2,1] => 1
001000111 => [2,1,3,3] => 1
001001000 => [2,1,2,1,3] => 2
001001001 => [2,1,2,1,2,1] => 2
001001010 => [2,1,2,1,1,1,1] => 1
001001011 => [2,1,2,1,1,2] => 2
001001100 => [2,1,2,2,2] => 1
001001101 => [2,1,2,2,1,1] => 1
001001110 => [2,1,2,3,1] => 2
001001111 => [2,1,2,4] => 2
001010000 => [2,1,1,1,4] => 1
001010001 => [2,1,1,1,3,1] => 1
001010010 => [2,1,1,1,2,1,1] => 1
001010011 => [2,1,1,1,2,2] => 1
001010100 => [2,1,1,1,1,1,2] => 1
001010101 => [2,1,1,1,1,1,1,1] => 0
001010110 => [2,1,1,1,1,2,1] => 1
001010111 => [2,1,1,1,1,3] => 1
001011000 => [2,1,1,2,3] => 2
001011001 => [2,1,1,2,2,1] => 1
001011010 => [2,1,1,2,1,1,1] => 1
001011011 => [2,1,1,2,1,2] => 2
001011100 => [2,1,1,3,2] => 1
001011101 => [2,1,1,3,1,1] => 1
001011110 => [2,1,1,4,1] => 1
001011111 => [2,1,1,5] => 1
001100000 => [2,2,5] => 1
001100001 => [2,2,4,1] => 1
001100010 => [2,2,3,1,1] => 1
001100011 => [2,2,3,2] => 1
001100100 => [2,2,2,1,2] => 1
001100101 => [2,2,2,1,1,1] => 0
001100110 => [2,2,2,2,1] => 0
001100111 => [2,2,2,3] => 1
001101000 => [2,2,1,1,3] => 1
001101001 => [2,2,1,1,2,1] => 1
001101010 => [2,2,1,1,1,1,1] => 0
001101011 => [2,2,1,1,1,2] => 1
001101100 => [2,2,1,2,2] => 1
001101101 => [2,2,1,2,1,1] => 1
001101110 => [2,2,1,3,1] => 1
001101111 => [2,2,1,4] => 1
001110000 => [2,3,4] => 2
001110001 => [2,3,3,1] => 1
001110010 => [2,3,2,1,1] => 1
001110011 => [2,3,2,2] => 1
001110100 => [2,3,1,1,2] => 2
001110101 => [2,3,1,1,1,1] => 1
001110110 => [2,3,1,2,1] => 2
001110111 => [2,3,1,3] => 2
001111000 => [2,4,3] => 1
001111001 => [2,4,2,1] => 1
001111010 => [2,4,1,1,1] => 1
001111011 => [2,4,1,2] => 2
001111100 => [2,5,2] => 1
001111101 => [2,5,1,1] => 1
001111110 => [2,6,1] => 1
001111111 => [2,7] => 1
010000000 => [1,1,7] => 1
010000001 => [1,1,6,1] => 1
010000010 => [1,1,5,1,1] => 1
010000011 => [1,1,5,2] => 1
010000100 => [1,1,4,1,2] => 2
010000101 => [1,1,4,1,1,1] => 1
010000110 => [1,1,4,2,1] => 1
010000111 => [1,1,4,3] => 1
010001000 => [1,1,3,1,3] => 2
010001001 => [1,1,3,1,2,1] => 2
010001010 => [1,1,3,1,1,1,1] => 1
010001011 => [1,1,3,1,1,2] => 2
010001100 => [1,1,3,2,2] => 1
010001101 => [1,1,3,2,1,1] => 1
010001110 => [1,1,3,3,1] => 1
010001111 => [1,1,3,4] => 2
010010000 => [1,1,2,1,4] => 2
010010001 => [1,1,2,1,3,1] => 2
010010010 => [1,1,2,1,2,1,1] => 2
010010011 => [1,1,2,1,2,2] => 2
010010100 => [1,1,2,1,1,1,2] => 2
010010101 => [1,1,2,1,1,1,1,1] => 1
010010110 => [1,1,2,1,1,2,1] => 2
010010111 => [1,1,2,1,1,3] => 2
010011000 => [1,1,2,2,3] => 2
010011001 => [1,1,2,2,2,1] => 1
010011010 => [1,1,2,2,1,1,1] => 1
010011011 => [1,1,2,2,1,2] => 2
010011100 => [1,1,2,3,2] => 2
010011101 => [1,1,2,3,1,1] => 2
010011110 => [1,1,2,4,1] => 2
010011111 => [1,1,2,5] => 2
010100000 => [1,1,1,1,5] => 1
010100001 => [1,1,1,1,4,1] => 1
010100010 => [1,1,1,1,3,1,1] => 1
010100011 => [1,1,1,1,3,2] => 1
010100100 => [1,1,1,1,2,1,2] => 2
010100101 => [1,1,1,1,2,1,1,1] => 1
010100110 => [1,1,1,1,2,2,1] => 1
010100111 => [1,1,1,1,2,3] => 2
010101000 => [1,1,1,1,1,1,3] => 1
010101001 => [1,1,1,1,1,1,2,1] => 1
010101010 => [1,1,1,1,1,1,1,1,1] => 0
010101011 => [1,1,1,1,1,1,1,2] => 1
010101100 => [1,1,1,1,1,2,2] => 1
010101101 => [1,1,1,1,1,2,1,1] => 1
010101110 => [1,1,1,1,1,3,1] => 1
010101111 => [1,1,1,1,1,4] => 1
010110000 => [1,1,1,2,4] => 2
010110001 => [1,1,1,2,3,1] => 2
010110010 => [1,1,1,2,2,1,1] => 1
010110011 => [1,1,1,2,2,2] => 1
010110100 => [1,1,1,2,1,1,2] => 2
010110101 => [1,1,1,2,1,1,1,1] => 1
010110110 => [1,1,1,2,1,2,1] => 2
010110111 => [1,1,1,2,1,3] => 2
010111000 => [1,1,1,3,3] => 1
010111001 => [1,1,1,3,2,1] => 1
010111010 => [1,1,1,3,1,1,1] => 1
010111011 => [1,1,1,3,1,2] => 2
010111100 => [1,1,1,4,2] => 1
010111101 => [1,1,1,4,1,1] => 1
010111110 => [1,1,1,5,1] => 1
010111111 => [1,1,1,6] => 1
011000000 => [1,2,6] => 2
011000001 => [1,2,5,1] => 2
011000010 => [1,2,4,1,1] => 2
011000011 => [1,2,4,2] => 2
011000100 => [1,2,3,1,2] => 3
011000101 => [1,2,3,1,1,1] => 2
011000110 => [1,2,3,2,1] => 2
011000111 => [1,2,3,3] => 2
011001000 => [1,2,2,1,3] => 2
011001001 => [1,2,2,1,2,1] => 2
011001010 => [1,2,2,1,1,1,1] => 1
011001011 => [1,2,2,1,1,2] => 2
011001100 => [1,2,2,2,2] => 1
011001101 => [1,2,2,2,1,1] => 1
011001110 => [1,2,2,3,1] => 2
011001111 => [1,2,2,4] => 2
011010000 => [1,2,1,1,4] => 2
011010001 => [1,2,1,1,3,1] => 2
011010010 => [1,2,1,1,2,1,1] => 2
011010011 => [1,2,1,1,2,2] => 2
011010100 => [1,2,1,1,1,1,2] => 2
011010101 => [1,2,1,1,1,1,1,1] => 1
011010110 => [1,2,1,1,1,2,1] => 2
011010111 => [1,2,1,1,1,3] => 2
011011000 => [1,2,1,2,3] => 3
011011001 => [1,2,1,2,2,1] => 2
011011010 => [1,2,1,2,1,1,1] => 2
011011011 => [1,2,1,2,1,2] => 3
011011100 => [1,2,1,3,2] => 2
011011101 => [1,2,1,3,1,1] => 2
011011110 => [1,2,1,4,1] => 2
011011111 => [1,2,1,5] => 2
011100000 => [1,3,5] => 2
011100001 => [1,3,4,1] => 2
011100010 => [1,3,3,1,1] => 1
011100011 => [1,3,3,2] => 1
011100100 => [1,3,2,1,2] => 2
011100101 => [1,3,2,1,1,1] => 1
011100110 => [1,3,2,2,1] => 1
011100111 => [1,3,2,3] => 2
011101000 => [1,3,1,1,3] => 2
011101001 => [1,3,1,1,2,1] => 2
011101010 => [1,3,1,1,1,1,1] => 1
011101011 => [1,3,1,1,1,2] => 2
011101100 => [1,3,1,2,2] => 2
011101101 => [1,3,1,2,1,1] => 2
011101110 => [1,3,1,3,1] => 2
011101111 => [1,3,1,4] => 2
011110000 => [1,4,4] => 1
011110001 => [1,4,3,1] => 1
011110010 => [1,4,2,1,1] => 1
011110011 => [1,4,2,2] => 1
011110100 => [1,4,1,1,2] => 2
011110101 => [1,4,1,1,1,1] => 1
011110110 => [1,4,1,2,1] => 2
011110111 => [1,4,1,3] => 2
011111000 => [1,5,3] => 1
011111001 => [1,5,2,1] => 1
011111010 => [1,5,1,1,1] => 1
011111011 => [1,5,1,2] => 2
011111100 => [1,6,2] => 1
011111101 => [1,6,1,1] => 1
011111110 => [1,7,1] => 1
011111111 => [1,8] => 1
100000000 => [1,8] => 1
100000001 => [1,7,1] => 1
100000010 => [1,6,1,1] => 1
100000011 => [1,6,2] => 1
100000100 => [1,5,1,2] => 2
100000101 => [1,5,1,1,1] => 1
100000110 => [1,5,2,1] => 1
100000111 => [1,5,3] => 1
100001000 => [1,4,1,3] => 2
100001001 => [1,4,1,2,1] => 2
100001010 => [1,4,1,1,1,1] => 1
100001011 => [1,4,1,1,2] => 2
100001100 => [1,4,2,2] => 1
100001101 => [1,4,2,1,1] => 1
100001110 => [1,4,3,1] => 1
100001111 => [1,4,4] => 1
100010000 => [1,3,1,4] => 2
100010001 => [1,3,1,3,1] => 2
100010010 => [1,3,1,2,1,1] => 2
100010011 => [1,3,1,2,2] => 2
100010100 => [1,3,1,1,1,2] => 2
100010101 => [1,3,1,1,1,1,1] => 1
100010110 => [1,3,1,1,2,1] => 2
100010111 => [1,3,1,1,3] => 2
100011000 => [1,3,2,3] => 2
100011001 => [1,3,2,2,1] => 1
100011010 => [1,3,2,1,1,1] => 1
100011011 => [1,3,2,1,2] => 2
100011100 => [1,3,3,2] => 1
100011101 => [1,3,3,1,1] => 1
100011110 => [1,3,4,1] => 2
100011111 => [1,3,5] => 2
100100000 => [1,2,1,5] => 2
100100001 => [1,2,1,4,1] => 2
100100010 => [1,2,1,3,1,1] => 2
100100011 => [1,2,1,3,2] => 2
100100100 => [1,2,1,2,1,2] => 3
100100101 => [1,2,1,2,1,1,1] => 2
100100110 => [1,2,1,2,2,1] => 2
100100111 => [1,2,1,2,3] => 3
100101000 => [1,2,1,1,1,3] => 2
100101001 => [1,2,1,1,1,2,1] => 2
100101010 => [1,2,1,1,1,1,1,1] => 1
100101011 => [1,2,1,1,1,1,2] => 2
100101100 => [1,2,1,1,2,2] => 2
100101101 => [1,2,1,1,2,1,1] => 2
100101110 => [1,2,1,1,3,1] => 2
100101111 => [1,2,1,1,4] => 2
100110000 => [1,2,2,4] => 2
100110001 => [1,2,2,3,1] => 2
100110010 => [1,2,2,2,1,1] => 1
100110011 => [1,2,2,2,2] => 1
100110100 => [1,2,2,1,1,2] => 2
100110101 => [1,2,2,1,1,1,1] => 1
100110110 => [1,2,2,1,2,1] => 2
100110111 => [1,2,2,1,3] => 2
100111000 => [1,2,3,3] => 2
100111001 => [1,2,3,2,1] => 2
100111010 => [1,2,3,1,1,1] => 2
100111011 => [1,2,3,1,2] => 3
100111100 => [1,2,4,2] => 2
100111101 => [1,2,4,1,1] => 2
100111110 => [1,2,5,1] => 2
100111111 => [1,2,6] => 2
101000000 => [1,1,1,6] => 1
101000001 => [1,1,1,5,1] => 1
101000010 => [1,1,1,4,1,1] => 1
101000011 => [1,1,1,4,2] => 1
101000100 => [1,1,1,3,1,2] => 2
101000101 => [1,1,1,3,1,1,1] => 1
101000110 => [1,1,1,3,2,1] => 1
101000111 => [1,1,1,3,3] => 1
101001000 => [1,1,1,2,1,3] => 2
101001001 => [1,1,1,2,1,2,1] => 2
101001010 => [1,1,1,2,1,1,1,1] => 1
101001011 => [1,1,1,2,1,1,2] => 2
101001100 => [1,1,1,2,2,2] => 1
101001101 => [1,1,1,2,2,1,1] => 1
101001110 => [1,1,1,2,3,1] => 2
101001111 => [1,1,1,2,4] => 2
101010000 => [1,1,1,1,1,4] => 1
101010001 => [1,1,1,1,1,3,1] => 1
101010010 => [1,1,1,1,1,2,1,1] => 1
101010011 => [1,1,1,1,1,2,2] => 1
101010100 => [1,1,1,1,1,1,1,2] => 1
101010101 => [1,1,1,1,1,1,1,1,1] => 0
101010110 => [1,1,1,1,1,1,2,1] => 1
101010111 => [1,1,1,1,1,1,3] => 1
101011000 => [1,1,1,1,2,3] => 2
101011001 => [1,1,1,1,2,2,1] => 1
101011010 => [1,1,1,1,2,1,1,1] => 1
101011011 => [1,1,1,1,2,1,2] => 2
101011100 => [1,1,1,1,3,2] => 1
101011101 => [1,1,1,1,3,1,1] => 1
101011110 => [1,1,1,1,4,1] => 1
101011111 => [1,1,1,1,5] => 1
101100000 => [1,1,2,5] => 2
101100001 => [1,1,2,4,1] => 2
101100010 => [1,1,2,3,1,1] => 2
101100011 => [1,1,2,3,2] => 2
101100100 => [1,1,2,2,1,2] => 2
101100101 => [1,1,2,2,1,1,1] => 1
101100110 => [1,1,2,2,2,1] => 1
101100111 => [1,1,2,2,3] => 2
101101000 => [1,1,2,1,1,3] => 2
101101001 => [1,1,2,1,1,2,1] => 2
101101010 => [1,1,2,1,1,1,1,1] => 1
101101011 => [1,1,2,1,1,1,2] => 2
101101100 => [1,1,2,1,2,2] => 2
101101101 => [1,1,2,1,2,1,1] => 2
101101110 => [1,1,2,1,3,1] => 2
101101111 => [1,1,2,1,4] => 2
101110000 => [1,1,3,4] => 2
101110001 => [1,1,3,3,1] => 1
101110010 => [1,1,3,2,1,1] => 1
101110011 => [1,1,3,2,2] => 1
101110100 => [1,1,3,1,1,2] => 2
101110101 => [1,1,3,1,1,1,1] => 1
101110110 => [1,1,3,1,2,1] => 2
101110111 => [1,1,3,1,3] => 2
101111000 => [1,1,4,3] => 1
101111001 => [1,1,4,2,1] => 1
101111010 => [1,1,4,1,1,1] => 1
101111011 => [1,1,4,1,2] => 2
101111100 => [1,1,5,2] => 1
101111101 => [1,1,5,1,1] => 1
101111110 => [1,1,6,1] => 1
101111111 => [1,1,7] => 1
110000000 => [2,7] => 1
110000001 => [2,6,1] => 1
110000010 => [2,5,1,1] => 1
110000011 => [2,5,2] => 1
110000100 => [2,4,1,2] => 2
110000101 => [2,4,1,1,1] => 1
110000110 => [2,4,2,1] => 1
110000111 => [2,4,3] => 1
110001000 => [2,3,1,3] => 2
110001001 => [2,3,1,2,1] => 2
110001010 => [2,3,1,1,1,1] => 1
110001011 => [2,3,1,1,2] => 2
110001100 => [2,3,2,2] => 1
110001101 => [2,3,2,1,1] => 1
110001110 => [2,3,3,1] => 1
110001111 => [2,3,4] => 2
110010000 => [2,2,1,4] => 1
110010001 => [2,2,1,3,1] => 1
110010010 => [2,2,1,2,1,1] => 1
110010011 => [2,2,1,2,2] => 1
110010100 => [2,2,1,1,1,2] => 1
110010101 => [2,2,1,1,1,1,1] => 0
110010110 => [2,2,1,1,2,1] => 1
110010111 => [2,2,1,1,3] => 1
110011000 => [2,2,2,3] => 1
110011001 => [2,2,2,2,1] => 0
110011010 => [2,2,2,1,1,1] => 0
110011011 => [2,2,2,1,2] => 1
110011100 => [2,2,3,2] => 1
110011101 => [2,2,3,1,1] => 1
110011110 => [2,2,4,1] => 1
110011111 => [2,2,5] => 1
110100000 => [2,1,1,5] => 1
110100001 => [2,1,1,4,1] => 1
110100010 => [2,1,1,3,1,1] => 1
110100011 => [2,1,1,3,2] => 1
110100100 => [2,1,1,2,1,2] => 2
110100101 => [2,1,1,2,1,1,1] => 1
110100110 => [2,1,1,2,2,1] => 1
110100111 => [2,1,1,2,3] => 2
110101000 => [2,1,1,1,1,3] => 1
110101001 => [2,1,1,1,1,2,1] => 1
110101010 => [2,1,1,1,1,1,1,1] => 0
110101011 => [2,1,1,1,1,1,2] => 1
110101100 => [2,1,1,1,2,2] => 1
110101101 => [2,1,1,1,2,1,1] => 1
110101110 => [2,1,1,1,3,1] => 1
110101111 => [2,1,1,1,4] => 1
110110000 => [2,1,2,4] => 2
110110001 => [2,1,2,3,1] => 2
110110010 => [2,1,2,2,1,1] => 1
110110011 => [2,1,2,2,2] => 1
110110100 => [2,1,2,1,1,2] => 2
110110101 => [2,1,2,1,1,1,1] => 1
110110110 => [2,1,2,1,2,1] => 2
110110111 => [2,1,2,1,3] => 2
110111000 => [2,1,3,3] => 1
110111001 => [2,1,3,2,1] => 1
110111010 => [2,1,3,1,1,1] => 1
110111011 => [2,1,3,1,2] => 2
110111100 => [2,1,4,2] => 1
110111101 => [2,1,4,1,1] => 1
110111110 => [2,1,5,1] => 1
110111111 => [2,1,6] => 1
111000000 => [3,6] => 1
111000001 => [3,5,1] => 1
111000010 => [3,4,1,1] => 1
111000011 => [3,4,2] => 1
111000100 => [3,3,1,2] => 1
111000101 => [3,3,1,1,1] => 0
111000110 => [3,3,2,1] => 0
111000111 => [3,3,3] => 0
111001000 => [3,2,1,3] => 1
111001001 => [3,2,1,2,1] => 1
111001010 => [3,2,1,1,1,1] => 0
111001011 => [3,2,1,1,2] => 1
111001100 => [3,2,2,2] => 0
111001101 => [3,2,2,1,1] => 0
111001110 => [3,2,3,1] => 1
111001111 => [3,2,4] => 1
111010000 => [3,1,1,4] => 1
111010001 => [3,1,1,3,1] => 1
111010010 => [3,1,1,2,1,1] => 1
111010011 => [3,1,1,2,2] => 1
111010100 => [3,1,1,1,1,2] => 1
111010101 => [3,1,1,1,1,1,1] => 0
111010110 => [3,1,1,1,2,1] => 1
111010111 => [3,1,1,1,3] => 1
111011000 => [3,1,2,3] => 2
111011001 => [3,1,2,2,1] => 1
111011010 => [3,1,2,1,1,1] => 1
111011011 => [3,1,2,1,2] => 2
111011100 => [3,1,3,2] => 1
111011101 => [3,1,3,1,1] => 1
111011110 => [3,1,4,1] => 1
111011111 => [3,1,5] => 1
111100000 => [4,5] => 1
111100001 => [4,4,1] => 0
111100010 => [4,3,1,1] => 0
111100011 => [4,3,2] => 0
111100100 => [4,2,1,2] => 1
111100101 => [4,2,1,1,1] => 0
111100110 => [4,2,2,1] => 0
111100111 => [4,2,3] => 1
111101000 => [4,1,1,3] => 1
111101001 => [4,1,1,2,1] => 1
111101010 => [4,1,1,1,1,1] => 0
111101011 => [4,1,1,1,2] => 1
111101100 => [4,1,2,2] => 1
111101101 => [4,1,2,1,1] => 1
111101110 => [4,1,3,1] => 1
111101111 => [4,1,4] => 1
111110000 => [5,4] => 0
111110001 => [5,3,1] => 0
111110010 => [5,2,1,1] => 0
111110011 => [5,2,2] => 0
111110100 => [5,1,1,2] => 1
111110101 => [5,1,1,1,1] => 0
111110110 => [5,1,2,1] => 1
111110111 => [5,1,3] => 1
111111000 => [6,3] => 0
111111001 => [6,2,1] => 0
111111010 => [6,1,1,1] => 0
111111011 => [6,1,2] => 1
111111100 => [7,2] => 0
111111101 => [7,1,1] => 0
111111110 => [8,1] => 0
111111111 => [9] => 0
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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:
6,2 10,6 14,18 22,38,4 30,82,16 44,154,58 60,284,162,6
$F_{1} = 2$
$F_{2} = 4$
$F_{3} = 6 + 2\ q$
$F_{4} = 10 + 6\ q$
$F_{5} = 14 + 18\ q$
$F_{6} = 22 + 38\ q + 4\ q^{2}$
$F_{7} = 30 + 82\ q + 16\ q^{2}$
$F_{8} = 44 + 154\ q + 58\ q^{2}$
$F_{9} = 60 + 284\ q + 162\ q^{2} + 6\ q^{3}$
Description
The number of ascents in an integer composition.
A composition has an ascent, or rise, at position $i$ if $a_i < a_{i+1}$.
A composition has an ascent, or rise, at position $i$ if $a_i < a_{i+1}$.
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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