Identifier
-
Mp00278:
Binary words
—rowmotion⟶
Binary words
St001437: Binary words ⟶ ℤ
Values
0 => 0 => 1
1 => 1 => 1
00 => 00 => 2
01 => 10 => 2
10 => 01 => 1
11 => 11 => 2
000 => 000 => 3
001 => 010 => 2
010 => 100 => 3
011 => 101 => 2
100 => 001 => 1
101 => 110 => 3
110 => 011 => 1
111 => 111 => 3
0000 => 0000 => 4
0001 => 0010 => 2
0010 => 0100 => 3
0011 => 0101 => 2
0100 => 1000 => 4
0101 => 1010 => 4
0110 => 1001 => 3
0111 => 1011 => 2
1000 => 0001 => 1
1001 => 0110 => 2
1010 => 1100 => 4
1011 => 1101 => 3
1100 => 0011 => 1
1101 => 1110 => 4
1110 => 0111 => 1
1111 => 1111 => 4
00000 => 00000 => 5
00001 => 00010 => 2
00010 => 00100 => 3
00011 => 00101 => 1
00100 => 01000 => 4
00101 => 01010 => 3
00110 => 01001 => 2
00111 => 01011 => 1
01000 => 10000 => 5
01001 => 10010 => 4
01010 => 10100 => 5
01011 => 10101 => 3
01100 => 10001 => 4
01101 => 10110 => 4
01110 => 10011 => 3
01111 => 10111 => 2
10000 => 00001 => 1
10001 => 00110 => 2
10010 => 01100 => 3
10011 => 01101 => 2
10100 => 11000 => 5
10101 => 11010 => 5
10110 => 11001 => 4
10111 => 11011 => 3
11000 => 00011 => 1
11001 => 01110 => 2
11010 => 11100 => 5
11011 => 11101 => 4
11100 => 00111 => 1
11101 => 11110 => 5
11110 => 01111 => 1
11111 => 11111 => 5
000000 => 000000 => 6
000001 => 000010 => 2
000010 => 000100 => 3
000011 => 000101 => 1
000100 => 001000 => 4
000101 => 001010 => 2
000110 => 001001 => 2
000111 => 001011 => 1
001000 => 010000 => 5
001001 => 010010 => 4
001010 => 010100 => 4
001011 => 010101 => 3
001100 => 010001 => 3
001101 => 010110 => 2
001110 => 010011 => 2
001111 => 010111 => 1
010000 => 100000 => 6
010001 => 100010 => 5
010010 => 100100 => 6
010011 => 100101 => 4
010100 => 101000 => 6
010101 => 101010 => 6
010110 => 101001 => 5
010111 => 101011 => 3
011000 => 100001 => 5
011001 => 100110 => 4
011010 => 101100 => 5
011011 => 101101 => 4
011100 => 100011 => 4
011101 => 101110 => 4
011110 => 100111 => 3
011111 => 101111 => 2
100000 => 000001 => 1
100001 => 000110 => 2
100010 => 001100 => 3
100011 => 001101 => 1
100100 => 011000 => 4
100101 => 011010 => 3
100110 => 011001 => 3
>>> Load all 1273 entries. <<<100111 => 011011 => 2
101000 => 110000 => 6
101001 => 110010 => 6
101010 => 110100 => 6
101011 => 110101 => 5
101100 => 110001 => 5
101101 => 110110 => 6
101110 => 110011 => 4
101111 => 110111 => 3
110000 => 000011 => 1
110001 => 001110 => 2
110010 => 011100 => 3
110011 => 011101 => 2
110100 => 111000 => 6
110101 => 111010 => 6
110110 => 111001 => 5
110111 => 111011 => 4
111000 => 000111 => 1
111001 => 011110 => 2
111010 => 111100 => 6
111011 => 111101 => 5
111100 => 001111 => 1
111101 => 111110 => 6
111110 => 011111 => 1
111111 => 111111 => 6
0000000 => 0000000 => 7
0000001 => 0000010 => 2
0000010 => 0000100 => 3
0000011 => 0000101 => 1
0000100 => 0001000 => 4
0000101 => 0001010 => 2
0000110 => 0001001 => 1
0000111 => 0001011 => 1
0001000 => 0010000 => 5
0001001 => 0010010 => 3
0001010 => 0010100 => 3
0001011 => 0010101 => 1
0001100 => 0010001 => 2
0001101 => 0010110 => 2
0001110 => 0010011 => 1
0001111 => 0010111 => 1
0010000 => 0100000 => 6
0010001 => 0100010 => 4
0010010 => 0100100 => 5
0010011 => 0100101 => 2
0010100 => 0101000 => 5
0010101 => 0101010 => 4
0010110 => 0101001 => 3
0010111 => 0101011 => 1
0011000 => 0100001 => 4
0011001 => 0100110 => 3
0011010 => 0101100 => 3
0011011 => 0101101 => 2
0011100 => 0100011 => 3
0011101 => 0101110 => 2
0011110 => 0100111 => 2
0011111 => 0101111 => 1
0100000 => 1000000 => 7
0100001 => 1000010 => 6
0100010 => 1000100 => 6
0100011 => 1000101 => 5
0100100 => 1001000 => 7
0100101 => 1001010 => 5
0100110 => 1001001 => 5
0100111 => 1001011 => 4
0101000 => 1010000 => 7
0101001 => 1010010 => 6
0101010 => 1010100 => 7
0101011 => 1010101 => 4
0101100 => 1010001 => 6
0101101 => 1010110 => 5
0101110 => 1010011 => 5
0101111 => 1010111 => 3
0110000 => 1000001 => 6
0110001 => 1000110 => 5
0110010 => 1001100 => 6
0110011 => 1001101 => 4
0110100 => 1011000 => 6
0110101 => 1011010 => 6
0110110 => 1011001 => 5
0110111 => 1011011 => 3
0111000 => 1000011 => 5
0111001 => 1001110 => 4
0111010 => 1011100 => 5
0111011 => 1011101 => 4
0111100 => 1000111 => 4
0111101 => 1011110 => 4
0111110 => 1001111 => 3
0111111 => 1011111 => 2
1000000 => 0000001 => 1
1000001 => 0000110 => 2
1000010 => 0001100 => 3
1000011 => 0001101 => 1
1000100 => 0011000 => 4
1000101 => 0011010 => 2
1000110 => 0011001 => 2
1000111 => 0011011 => 1
1001000 => 0110000 => 5
1001001 => 0110010 => 4
1001010 => 0110100 => 4
1001011 => 0110101 => 3
1001100 => 0110001 => 4
1001101 => 0110110 => 3
1001110 => 0110011 => 2
1001111 => 0110111 => 1
1010000 => 1100000 => 7
1010001 => 1100010 => 7
1010010 => 1100100 => 7
1010011 => 1100101 => 6
1010100 => 1101000 => 7
1010101 => 1101010 => 7
1010110 => 1101001 => 6
1010111 => 1101011 => 5
1011000 => 1100001 => 6
1011001 => 1100110 => 6
1011010 => 1101100 => 7
1011011 => 1101101 => 5
1011100 => 1100011 => 5
1011101 => 1101110 => 6
1011110 => 1100111 => 4
1011111 => 1101111 => 3
1100000 => 0000011 => 1
1100001 => 0001110 => 2
1100010 => 0011100 => 3
1100011 => 0011101 => 1
1100100 => 0111000 => 4
1100101 => 0111010 => 3
1100110 => 0111001 => 3
1100111 => 0111011 => 2
1101000 => 1110000 => 7
1101001 => 1110010 => 7
1101010 => 1110100 => 7
1101011 => 1110101 => 6
1101100 => 1110001 => 6
1101101 => 1110110 => 7
1101110 => 1110011 => 5
1101111 => 1110111 => 4
1110000 => 0000111 => 1
1110001 => 0011110 => 2
1110010 => 0111100 => 3
1110011 => 0111101 => 2
1110100 => 1111000 => 7
1110101 => 1111010 => 7
1110110 => 1111001 => 6
1110111 => 1111011 => 5
1111000 => 0001111 => 1
1111001 => 0111110 => 2
1111010 => 1111100 => 7
1111011 => 1111101 => 6
1111100 => 0011111 => 1
1111101 => 1111110 => 7
1111110 => 0111111 => 1
1111111 => 1111111 => 7
00000000 => 00000000 => 8
00000001 => 00000010 => 2
00000010 => 00000100 => 3
00000011 => 00000101 => 1
00000100 => 00001000 => 4
00000101 => 00001010 => 2
00000110 => 00001001 => 1
00000111 => 00001011 => 1
00001000 => 00010000 => 5
00001001 => 00010010 => 2
00001010 => 00010100 => 3
00001011 => 00010101 => 1
00001100 => 00010001 => 2
00001101 => 00010110 => 2
00001110 => 00010011 => 1
00001111 => 00010111 => 1
00010000 => 00100000 => 6
00010001 => 00100010 => 4
00010010 => 00100100 => 4
00010011 => 00100101 => 1
00010100 => 00101000 => 4
00010101 => 00101010 => 2
00010110 => 00101001 => 2
00010111 => 00101011 => 1
00011000 => 00100001 => 3
00011001 => 00100110 => 2
00011010 => 00101100 => 3
00011011 => 00101101 => 1
00011100 => 00100011 => 2
00011101 => 00101110 => 2
00011110 => 00100111 => 1
00011111 => 00101111 => 1
00100000 => 01000000 => 7
00100001 => 01000010 => 5
00100010 => 01000100 => 6
00100011 => 01000101 => 3
00100100 => 01001000 => 6
00100101 => 01001010 => 4
00100110 => 01001001 => 3
00100111 => 01001011 => 2
00101000 => 01010000 => 6
00101001 => 01010010 => 5
00101010 => 01010100 => 5
00101011 => 01010101 => 4
00101100 => 01010001 => 4
00101101 => 01010110 => 2
00101110 => 01010011 => 3
00101111 => 01010111 => 1
00110000 => 01000001 => 5
00110001 => 01000110 => 4
00110010 => 01001100 => 4
00110011 => 01001101 => 2
00110100 => 01011000 => 4
00110101 => 01011010 => 3
00110110 => 01011001 => 3
00110111 => 01011011 => 1
00111000 => 01000011 => 4
00111001 => 01001110 => 3
00111010 => 01011100 => 3
00111011 => 01011101 => 2
00111100 => 01000111 => 3
00111101 => 01011110 => 2
00111110 => 01001111 => 2
00111111 => 01011111 => 1
01000000 => 10000000 => 8
01000001 => 10000010 => 7
01000010 => 10000100 => 7
01000011 => 10000101 => 6
01000100 => 10001000 => 8
01000101 => 10001010 => 6
01000110 => 10001001 => 6
01000111 => 10001011 => 5
01001000 => 10010000 => 8
01001001 => 10010010 => 6
01001010 => 10010100 => 7
01001011 => 10010101 => 5
01001100 => 10010001 => 7
01001101 => 10010110 => 5
01001110 => 10010011 => 5
01001111 => 10010111 => 4
01010000 => 10100000 => 8
01010001 => 10100010 => 7
01010010 => 10100100 => 8
01010011 => 10100101 => 6
01010100 => 10101000 => 8
01010101 => 10101010 => 8
01010110 => 10101001 => 7
01010111 => 10101011 => 4
01011000 => 10100001 => 7
01011001 => 10100110 => 6
01011010 => 10101100 => 6
01011011 => 10101101 => 4
01011100 => 10100011 => 6
01011101 => 10101110 => 5
01011110 => 10100111 => 5
01011111 => 10101111 => 3
01100000 => 10000001 => 7
01100001 => 10000110 => 6
01100010 => 10001100 => 6
01100011 => 10001101 => 5
01100100 => 10011000 => 7
01100101 => 10011010 => 5
01100110 => 10011001 => 6
01100111 => 10011011 => 4
01101000 => 10110000 => 7
01101001 => 10110010 => 7
01101010 => 10110100 => 7
01101011 => 10110101 => 5
01101100 => 10110001 => 6
01101101 => 10110110 => 6
01101110 => 10110011 => 5
01101111 => 10110111 => 3
01110000 => 10000011 => 6
01110001 => 10001110 => 5
01110010 => 10011100 => 6
01110011 => 10011101 => 4
01110100 => 10111000 => 6
01110101 => 10111010 => 6
01110110 => 10111001 => 5
01110111 => 10111011 => 4
01111000 => 10000111 => 5
01111001 => 10011110 => 4
01111010 => 10111100 => 5
01111011 => 10111101 => 4
01111100 => 10001111 => 4
01111101 => 10111110 => 4
01111110 => 10011111 => 3
01111111 => 10111111 => 2
10000000 => 00000001 => 1
10000001 => 00000110 => 2
10000010 => 00001100 => 3
10000011 => 00001101 => 1
10000100 => 00011000 => 4
10000101 => 00011010 => 2
10000110 => 00011001 => 1
10000111 => 00011011 => 1
10001000 => 00110000 => 5
10001001 => 00110010 => 3
10001010 => 00110100 => 3
10001011 => 00110101 => 1
10001100 => 00110001 => 3
10001101 => 00110110 => 2
10001110 => 00110011 => 2
10001111 => 00110111 => 1
10010000 => 01100000 => 6
10010001 => 01100010 => 5
10010010 => 01100100 => 5
10010011 => 01100101 => 4
10010100 => 01101000 => 5
10010101 => 01101010 => 4
10010110 => 01101001 => 4
10010111 => 01101011 => 2
10011000 => 01100001 => 5
10011001 => 01100110 => 4
10011010 => 01101100 => 4
10011011 => 01101101 => 3
10011100 => 01100011 => 3
10011101 => 01101110 => 2
10011110 => 01100111 => 2
10011111 => 01101111 => 1
10100000 => 11000000 => 8
10100001 => 11000010 => 8
10100010 => 11000100 => 8
10100011 => 11000101 => 7
10100100 => 11001000 => 8
10100101 => 11001010 => 8
10100110 => 11001001 => 7
10100111 => 11001011 => 6
10101000 => 11010000 => 8
10101001 => 11010010 => 8
10101010 => 11010100 => 8
10101011 => 11010101 => 7
10101100 => 11010001 => 7
10101101 => 11010110 => 7
10101110 => 11010011 => 6
10101111 => 11010111 => 5
10110000 => 11000001 => 7
10110001 => 11000110 => 7
10110010 => 11001100 => 8
10110011 => 11001101 => 6
10110100 => 11011000 => 8
10110101 => 11011010 => 8
10110110 => 11011001 => 7
10110111 => 11011011 => 5
10111000 => 11000011 => 6
10111001 => 11001110 => 6
10111010 => 11011100 => 7
10111011 => 11011101 => 6
10111100 => 11000111 => 5
10111101 => 11011110 => 6
10111110 => 11001111 => 4
10111111 => 11011111 => 3
11000000 => 00000011 => 1
11000001 => 00001110 => 2
11000010 => 00011100 => 3
11000011 => 00011101 => 1
11000100 => 00111000 => 4
11000101 => 00111010 => 2
11000110 => 00111001 => 2
11000111 => 00111011 => 1
11001000 => 01110000 => 5
11001001 => 01110010 => 4
11001010 => 01110100 => 4
11001011 => 01110101 => 3
11001100 => 01110001 => 4
11001101 => 01110110 => 3
11001110 => 01110011 => 3
11001111 => 01110111 => 2
11010000 => 11100000 => 8
11010001 => 11100010 => 8
11010010 => 11100100 => 8
11010011 => 11100101 => 7
11010100 => 11101000 => 8
11010101 => 11101010 => 8
11010110 => 11101001 => 7
11010111 => 11101011 => 6
11011000 => 11100001 => 7
11011001 => 11100110 => 8
11011010 => 11101100 => 8
11011011 => 11101101 => 7
11011100 => 11100011 => 6
11011101 => 11101110 => 8
11011110 => 11100111 => 5
11011111 => 11101111 => 4
11100000 => 00000111 => 1
11100001 => 00011110 => 2
11100010 => 00111100 => 3
11100011 => 00111101 => 1
11100100 => 01111000 => 4
11100101 => 01111010 => 3
11100110 => 01111001 => 3
11100111 => 01111011 => 2
11101000 => 11110000 => 8
11101001 => 11110010 => 8
11101010 => 11110100 => 8
11101011 => 11110101 => 7
11101100 => 11110001 => 7
11101101 => 11110110 => 8
11101110 => 11110011 => 6
11101111 => 11110111 => 5
11110000 => 00001111 => 1
11110001 => 00111110 => 2
11110010 => 01111100 => 3
11110011 => 01111101 => 2
11110100 => 11111000 => 8
11110101 => 11111010 => 8
11110110 => 11111001 => 7
11110111 => 11111011 => 6
11111000 => 00011111 => 1
11111001 => 01111110 => 2
11111010 => 11111100 => 8
11111011 => 11111101 => 7
11111100 => 00111111 => 1
11111101 => 11111110 => 8
11111110 => 01111111 => 1
11111111 => 11111111 => 8
000000000 => 000000000 => 9
000000001 => 000000010 => 2
000000010 => 000000100 => 3
000000011 => 000000101 => 1
000000100 => 000001000 => 4
000000101 => 000001010 => 2
000000110 => 000001001 => 1
000000111 => 000001011 => 1
000001000 => 000010000 => 5
000001001 => 000010010 => 2
000001010 => 000010100 => 3
000001011 => 000010101 => 1
000001100 => 000010001 => 1
000001101 => 000010110 => 2
000001110 => 000010011 => 1
000001111 => 000010111 => 1
000010000 => 000100000 => 6
000010001 => 000100010 => 3
000010010 => 000100100 => 3
000010011 => 000100101 => 1
000010100 => 000101000 => 4
000010101 => 000101010 => 2
000010110 => 000101001 => 1
000010111 => 000101011 => 1
000011000 => 000100001 => 2
000011001 => 000100110 => 2
000011010 => 000101100 => 3
000011011 => 000101101 => 1
000011100 => 000100011 => 1
000011101 => 000101110 => 2
000011110 => 000100111 => 1
000011111 => 000101111 => 1
000100000 => 001000000 => 7
000100001 => 001000010 => 4
000100010 => 001000100 => 5
000100011 => 001000101 => 2
000100100 => 001001000 => 5
000100101 => 001001010 => 2
000100110 => 001001001 => 3
000100111 => 001001011 => 1
000101000 => 001010000 => 5
000101001 => 001010010 => 3
000101010 => 001010100 => 3
000101011 => 001010101 => 1
000101100 => 001010001 => 3
000101101 => 001010110 => 2
000101110 => 001010011 => 1
000101111 => 001010111 => 1
000110000 => 001000001 => 4
000110001 => 001000110 => 3
000110010 => 001001100 => 3
000110011 => 001001101 => 1
000110100 => 001011000 => 4
000110101 => 001011010 => 2
000110110 => 001011001 => 2
000110111 => 001011011 => 1
000111000 => 001000011 => 3
000111001 => 001001110 => 2
000111010 => 001011100 => 3
000111011 => 001011101 => 1
000111100 => 001000111 => 2
000111101 => 001011110 => 2
000111110 => 001001111 => 1
000111111 => 001011111 => 1
001000000 => 010000000 => 8
001000001 => 010000010 => 6
001000010 => 010000100 => 6
001000011 => 010000101 => 4
001000100 => 010001000 => 7
001000101 => 010001010 => 4
001000110 => 010001001 => 4
001000111 => 010001011 => 3
001001000 => 010010000 => 7
001001001 => 010010010 => 6
001001010 => 010010100 => 5
001001011 => 010010101 => 2
001001100 => 010010001 => 5
001001101 => 010010110 => 3
001001110 => 010010011 => 3
001001111 => 010010111 => 2
001010000 => 010100000 => 7
001010001 => 010100010 => 6
001010010 => 010100100 => 6
001010011 => 010100101 => 3
001010100 => 010101000 => 6
001010101 => 010101010 => 5
001010110 => 010101001 => 4
001010111 => 010101011 => 1
001011000 => 010100001 => 5
001011001 => 010100110 => 4
001011010 => 010101100 => 3
001011011 => 010101101 => 2
001011100 => 010100011 => 4
001011101 => 010101110 => 2
001011110 => 010100111 => 3
001011111 => 010101111 => 1
001100000 => 010000001 => 6
001100001 => 010000110 => 5
001100010 => 010001100 => 5
001100011 => 010001101 => 3
001100100 => 010011000 => 5
001100101 => 010011010 => 4
001100110 => 010011001 => 3
001100111 => 010011011 => 2
001101000 => 010110000 => 5
001101001 => 010110010 => 4
001101010 => 010110100 => 4
001101011 => 010110101 => 3
001101100 => 010110001 => 4
001101101 => 010110110 => 2
001101110 => 010110011 => 2
001101111 => 010110111 => 1
001110000 => 010000011 => 5
001110001 => 010001110 => 4
001110010 => 010011100 => 4
001110011 => 010011101 => 2
001110100 => 010111000 => 4
001110101 => 010111010 => 3
001110110 => 010111001 => 3
001110111 => 010111011 => 1
001111000 => 010000111 => 4
001111001 => 010011110 => 3
001111010 => 010111100 => 3
001111011 => 010111101 => 2
001111100 => 010001111 => 3
001111101 => 010111110 => 2
001111110 => 010011111 => 2
001111111 => 010111111 => 1
010000000 => 100000000 => 9
010000001 => 100000010 => 8
010000010 => 100000100 => 8
010000011 => 100000101 => 7
010000100 => 100001000 => 8
010000101 => 100001010 => 7
010000110 => 100001001 => 7
010000111 => 100001011 => 6
010001000 => 100010000 => 9
010001001 => 100010010 => 7
010001010 => 100010100 => 7
010001011 => 100010101 => 6
010001100 => 100010001 => 7
010001101 => 100010110 => 6
010001110 => 100010011 => 6
010001111 => 100010111 => 5
010010000 => 100100000 => 9
010010001 => 100100010 => 8
010010010 => 100100100 => 9
010010011 => 100100101 => 6
010010100 => 100101000 => 8
010010101 => 100101010 => 6
010010110 => 100101001 => 6
010010111 => 100101011 => 5
010011000 => 100100001 => 8
010011001 => 100100110 => 6
010011010 => 100101100 => 7
010011011 => 100101101 => 5
010011100 => 100100011 => 7
010011101 => 100101110 => 5
010011110 => 100100111 => 5
010011111 => 100101111 => 4
010100000 => 101000000 => 9
010100001 => 101000010 => 8
010100010 => 101000100 => 9
010100011 => 101000101 => 7
010100100 => 101001000 => 9
010100101 => 101001010 => 7
010100110 => 101001001 => 8
010100111 => 101001011 => 6
010101000 => 101010000 => 9
010101001 => 101010010 => 8
010101010 => 101010100 => 9
010101011 => 101010101 => 5
010101100 => 101010001 => 8
010101101 => 101010110 => 6
010101110 => 101010011 => 7
010101111 => 101010111 => 4
010110000 => 101000001 => 8
010110001 => 101000110 => 7
010110010 => 101001100 => 8
010110011 => 101001101 => 6
010110100 => 101011000 => 7
010110101 => 101011010 => 7
010110110 => 101011001 => 6
010110111 => 101011011 => 4
010111000 => 101000011 => 7
010111001 => 101001110 => 6
010111010 => 101011100 => 6
010111011 => 101011101 => 4
010111100 => 101000111 => 6
010111101 => 101011110 => 5
010111110 => 101001111 => 5
010111111 => 101011111 => 3
011000000 => 100000001 => 8
011000001 => 100000110 => 7
011000010 => 100001100 => 7
011000011 => 100001101 => 6
011000100 => 100011000 => 8
011000101 => 100011010 => 6
011000110 => 100011001 => 6
011000111 => 100011011 => 5
011001000 => 100110000 => 8
011001001 => 100110010 => 7
011001010 => 100110100 => 7
011001011 => 100110101 => 5
011001100 => 100110001 => 7
011001101 => 100110110 => 5
011001110 => 100110011 => 5
011001111 => 100110111 => 4
011010000 => 101100000 => 8
011010001 => 101100010 => 8
011010010 => 101100100 => 8
011010011 => 101100101 => 6
011010100 => 101101000 => 8
011010101 => 101101010 => 8
011010110 => 101101001 => 7
011010111 => 101101011 => 5
011011000 => 101100001 => 7
011011001 => 101100110 => 7
011011010 => 101101100 => 7
011011011 => 101101101 => 6
011011100 => 101100011 => 6
011011101 => 101101110 => 5
011011110 => 101100111 => 5
011011111 => 101101111 => 3
011100000 => 100000011 => 7
011100001 => 100001110 => 6
011100010 => 100011100 => 6
011100011 => 100011101 => 5
011100100 => 100111000 => 7
011100101 => 100111010 => 5
011100110 => 100111001 => 6
011100111 => 100111011 => 4
011101000 => 101110000 => 7
011101001 => 101110010 => 7
011101010 => 101110100 => 7
011101011 => 101110101 => 6
011101100 => 101110001 => 6
011101101 => 101110110 => 6
011101110 => 101110011 => 5
011101111 => 101110111 => 3
011110000 => 100000111 => 6
011110001 => 100011110 => 5
011110010 => 100111100 => 6
011110011 => 100111101 => 4
011110100 => 101111000 => 6
011110101 => 101111010 => 6
011110110 => 101111001 => 5
011110111 => 101111011 => 4
011111000 => 100001111 => 5
011111001 => 100111110 => 4
011111010 => 101111100 => 5
011111011 => 101111101 => 4
011111100 => 100011111 => 4
011111101 => 101111110 => 4
011111110 => 100111111 => 3
011111111 => 101111111 => 2
100000000 => 000000001 => 1
100000001 => 000000110 => 2
100000010 => 000001100 => 3
100000011 => 000001101 => 1
100000100 => 000011000 => 4
100000101 => 000011010 => 2
100000110 => 000011001 => 1
100000111 => 000011011 => 1
100001000 => 000110000 => 5
100001001 => 000110010 => 2
100001010 => 000110100 => 3
100001011 => 000110101 => 1
100001100 => 000110001 => 2
100001101 => 000110110 => 2
100001110 => 000110011 => 1
100001111 => 000110111 => 1
100010000 => 001100000 => 6
100010001 => 001100010 => 4
100010010 => 001100100 => 4
100010011 => 001100101 => 2
100010100 => 001101000 => 4
100010101 => 001101010 => 2
100010110 => 001101001 => 2
100010111 => 001101011 => 1
100011000 => 001100001 => 4
100011001 => 001100110 => 3
100011010 => 001101100 => 3
100011011 => 001101101 => 1
100011100 => 001100011 => 2
100011101 => 001101110 => 2
100011110 => 001100111 => 1
100011111 => 001101111 => 1
100100000 => 011000000 => 7
100100001 => 011000010 => 6
100100010 => 011000100 => 6
100100011 => 011000101 => 5
100100100 => 011001000 => 6
100100101 => 011001010 => 5
100100110 => 011001001 => 5
100100111 => 011001011 => 3
100101000 => 011010000 => 6
100101001 => 011010010 => 5
100101010 => 011010100 => 5
100101011 => 011010101 => 4
100101100 => 011010001 => 5
100101101 => 011010110 => 4
100101110 => 011010011 => 3
100101111 => 011010111 => 2
100110000 => 011000001 => 6
100110001 => 011000110 => 4
100110010 => 011001100 => 5
100110011 => 011001101 => 3
100110100 => 011011000 => 5
100110101 => 011011010 => 4
100110110 => 011011001 => 4
100110111 => 011011011 => 3
100111000 => 011000011 => 4
100111001 => 011001110 => 3
100111010 => 011011100 => 3
100111011 => 011011101 => 2
100111100 => 011000111 => 3
100111101 => 011011110 => 2
100111110 => 011001111 => 2
100111111 => 011011111 => 1
101000000 => 110000000 => 9
101000001 => 110000010 => 9
101000010 => 110000100 => 9
101000011 => 110000101 => 8
101000100 => 110001000 => 9
101000101 => 110001010 => 9
101000110 => 110001001 => 8
101000111 => 110001011 => 7
101001000 => 110010000 => 9
101001001 => 110010010 => 9
101001010 => 110010100 => 9
101001011 => 110010101 => 8
101001100 => 110010001 => 8
101001101 => 110010110 => 8
101001110 => 110010011 => 7
101001111 => 110010111 => 6
101010000 => 110100000 => 9
101010001 => 110100010 => 9
101010010 => 110100100 => 9
101010011 => 110100101 => 8
101010100 => 110101000 => 9
101010101 => 110101010 => 9
101010110 => 110101001 => 8
101010111 => 110101011 => 7
101011000 => 110100001 => 8
101011001 => 110100110 => 8
101011010 => 110101100 => 9
101011011 => 110101101 => 7
101011100 => 110100011 => 7
101011101 => 110101110 => 7
101011110 => 110100111 => 6
101011111 => 110101111 => 5
101100000 => 110000001 => 8
101100001 => 110000110 => 8
101100010 => 110001100 => 8
101100011 => 110001101 => 7
101100100 => 110011000 => 9
101100101 => 110011010 => 8
101100110 => 110011001 => 7
101100111 => 110011011 => 6
101101000 => 110110000 => 9
101101001 => 110110010 => 9
101101010 => 110110100 => 9
101101011 => 110110101 => 8
101101100 => 110110001 => 8
101101101 => 110110110 => 9
101101110 => 110110011 => 7
101101111 => 110110111 => 5
101110000 => 110000011 => 7
101110001 => 110001110 => 7
101110010 => 110011100 => 8
101110011 => 110011101 => 6
101110100 => 110111000 => 8
101110101 => 110111010 => 8
101110110 => 110111001 => 7
101110111 => 110111011 => 5
101111000 => 110000111 => 6
101111001 => 110011110 => 6
101111010 => 110111100 => 7
101111011 => 110111101 => 6
101111100 => 110001111 => 5
101111101 => 110111110 => 6
101111110 => 110011111 => 4
101111111 => 110111111 => 3
110000000 => 000000011 => 1
110000001 => 000001110 => 2
110000010 => 000011100 => 3
110000011 => 000011101 => 1
110000100 => 000111000 => 4
110000101 => 000111010 => 2
110000110 => 000111001 => 1
110000111 => 000111011 => 1
110001000 => 001110000 => 5
110001001 => 001110010 => 3
110001010 => 001110100 => 3
110001011 => 001110101 => 1
110001100 => 001110001 => 3
110001101 => 001110110 => 2
110001110 => 001110011 => 2
110001111 => 001110111 => 1
110010000 => 011100000 => 6
110010001 => 011100010 => 5
110010010 => 011100100 => 5
110010011 => 011100101 => 4
110010100 => 011101000 => 5
110010101 => 011101010 => 4
110010110 => 011101001 => 4
110010111 => 011101011 => 3
110011000 => 011100001 => 5
110011001 => 011100110 => 4
110011010 => 011101100 => 4
110011011 => 011101101 => 3
110011100 => 011100011 => 4
110011101 => 011101110 => 3
110011110 => 011100111 => 2
110011111 => 011101111 => 1
110100000 => 111000000 => 9
110100001 => 111000010 => 9
110100010 => 111000100 => 9
110100011 => 111000101 => 8
110100100 => 111001000 => 9
110100101 => 111001010 => 9
110100110 => 111001001 => 8
110100111 => 111001011 => 7
110101000 => 111010000 => 9
110101001 => 111010010 => 9
110101010 => 111010100 => 9
110101011 => 111010101 => 8
110101100 => 111010001 => 8
110101101 => 111010110 => 9
110101110 => 111010011 => 7
110101111 => 111010111 => 6
110110000 => 111000001 => 8
110110001 => 111000110 => 9
110110010 => 111001100 => 9
110110011 => 111001101 => 8
110110100 => 111011000 => 9
110110101 => 111011010 => 9
110110110 => 111011001 => 8
110110111 => 111011011 => 7
110111000 => 111000011 => 7
110111001 => 111001110 => 8
110111010 => 111011100 => 9
110111011 => 111011101 => 7
110111100 => 111000111 => 6
110111101 => 111011110 => 8
110111110 => 111001111 => 5
110111111 => 111011111 => 4
111000000 => 000000111 => 1
111000001 => 000011110 => 2
111000010 => 000111100 => 3
111000011 => 000111101 => 1
111000100 => 001111000 => 4
111000101 => 001111010 => 2
111000110 => 001111001 => 2
111000111 => 001111011 => 1
111001000 => 011110000 => 5
111001001 => 011110010 => 4
111001010 => 011110100 => 4
111001011 => 011110101 => 3
111001100 => 011110001 => 4
111001101 => 011110110 => 3
111001110 => 011110011 => 3
111001111 => 011110111 => 2
111010000 => 111100000 => 9
111010001 => 111100010 => 9
111010010 => 111100100 => 9
111010011 => 111100101 => 8
111010100 => 111101000 => 9
111010101 => 111101010 => 9
111010110 => 111101001 => 8
111010111 => 111101011 => 7
111011000 => 111100001 => 8
111011001 => 111100110 => 9
111011010 => 111101100 => 9
111011011 => 111101101 => 8
111011100 => 111100011 => 7
111011101 => 111101110 => 9
111011110 => 111100111 => 6
111011111 => 111101111 => 5
111100000 => 000001111 => 1
111100001 => 000111110 => 2
111100010 => 001111100 => 3
111100011 => 001111101 => 1
111100100 => 011111000 => 4
111100101 => 011111010 => 3
111100110 => 011111001 => 3
111100111 => 011111011 => 2
111101000 => 111110000 => 9
111101001 => 111110010 => 9
111101010 => 111110100 => 9
111101011 => 111110101 => 8
111101100 => 111110001 => 8
111101101 => 111110110 => 9
111101110 => 111110011 => 7
111101111 => 111110111 => 6
111110000 => 000011111 => 1
111110001 => 001111110 => 2
111110010 => 011111100 => 3
111110011 => 011111101 => 2
111110100 => 111111000 => 9
111110101 => 111111010 => 9
111110110 => 111111001 => 8
111110111 => 111111011 => 7
111111000 => 000111111 => 1
111111001 => 011111110 => 2
111111010 => 111111100 => 9
111111011 => 111111101 => 8
111111100 => 001111111 => 1
111111101 => 111111110 => 9
111111110 => 011111111 => 1
111111111 => 111111111 => 9
1010101010 => 1101010100 => 10
1010101100 => 1101010001 => 9
1010110010 => 1101001100 => 10
1010110100 => 1101011000 => 10
1011001010 => 1100110100 => 9
1011001100 => 1100110001 => 9
1011010010 => 1101100100 => 10
1011010100 => 1101101000 => 10
1011011000 => 1101100001 => 9
1011100100 => 1100111000 => 9
1011101000 => 1101110000 => 9
1101001010 => 1110010100 => 10
1101001100 => 1110010001 => 9
1101010010 => 1110100100 => 10
1101010100 => 1110101000 => 10
1101011000 => 1110100001 => 9
1101100010 => 1110001100 => 10
1101100100 => 1110011000 => 10
1101101000 => 1110110000 => 10
1110100010 => 1111000100 => 10
1110100100 => 1111001000 => 10
1110101000 => 1111010000 => 10
1110110000 => 1111000001 => 9
1111010000 => 1111100000 => 10
101010101010 => 110101010100 => 12
101010110010 => 110101001100 => 12
101010110100 => 110101011000 => 12
101011001010 => 110100110100 => 12
101011010010 => 110101100100 => 12
101011010100 => 110101101000 => 12
101011100100 => 110100111000 => 11
101011101000 => 110101110000 => 11
101100101010 => 110011010100 => 11
101100110010 => 110011001100 => 12
101100110100 => 110011011000 => 11
101101001010 => 110110010100 => 12
101101010010 => 110110100100 => 12
101101010100 => 110110101000 => 12
101101100010 => 110110001100 => 12
101101100100 => 110110011000 => 12
101101101000 => 110110110000 => 12
101110010010 => 110011100100 => 11
101110010100 => 110011101000 => 10
101110100010 => 110111000100 => 11
101110100100 => 110111001000 => 11
101110101000 => 110111010000 => 11
101111001000 => 110011110000 => 10
101111010000 => 110111100000 => 10
110100101010 => 111001010100 => 12
110100110010 => 111001001100 => 12
110100110100 => 111001011000 => 12
110101001010 => 111010010100 => 12
110101010010 => 111010100100 => 12
110101010100 => 111010101000 => 12
110101100010 => 111010001100 => 12
110101100100 => 111010011000 => 12
110101101000 => 111010110000 => 12
110110001010 => 111000110100 => 12
110110010010 => 111001100100 => 12
110110010100 => 111001101000 => 12
110110100010 => 111011000100 => 12
110110100100 => 111011001000 => 12
110110101000 => 111011010000 => 12
110111000100 => 111000111000 => 12
110111001000 => 111001110000 => 12
110111010000 => 111011100000 => 12
111010001010 => 111100010100 => 12
111010010010 => 111100100100 => 12
111010010100 => 111100101000 => 12
111010100010 => 111101000100 => 12
111010100100 => 111101001000 => 12
111010101000 => 111101010000 => 12
111011000010 => 111100001100 => 12
111011000100 => 111100011000 => 12
111011001000 => 111100110000 => 12
111011010000 => 111101100000 => 12
111101000010 => 111110000100 => 12
111101000100 => 111110001000 => 12
111101001000 => 111110010000 => 12
111101010000 => 111110100000 => 12
111110100000 => 111111000000 => 12
10111110010000 => 11001111100000 => 11
11110110000010 => 11111000001100 => 14
1111111101 => 1111111110 => 10
1110100001 => 1111000010 => 10
1101010001 => 1110100010 => 10
1101001001 => 1110010010 => 10
1101000101 => 1110001010 => 10
1101000011 => 1110000101 => 9
1011111101 => 1101111110 => 6
1011010001 => 1101100010 => 10
1011001001 => 1100110010 => 10
1010101001 => 1101010010 => 10
1010100110 => 1101001001 => 9
1010100101 => 1101001010 => 10
1010011010 => 1100101100 => 9
1010011001 => 1100100110 => 9
1010010110 => 1100101001 => 9
1010010101 => 1100101010 => 10
0111111101 => 1011111110 => 4
0111111001 => 1001111110 => 4
0111110001 => 1000111110 => 5
0111100001 => 1000011110 => 6
0111000001 => 1000001110 => 7
0110000001 => 1000000110 => 8
0100000001 => 1000000010 => 9
01111111101 => 10111111110 => 4
0111111011 => 1011111101 => 4
01111111001 => 10011111110 => 4
01111110001 => 10001111110 => 5
01111100001 => 10000111110 => 6
0111010001 => 1011100010 => 8
01111000001 => 10000011110 => 7
01110000001 => 10000001110 => 8
01100000001 => 10000000110 => 9
01000000001 => 10000000010 => 10
0101010101 => 1010101010 => 10
0101010011 => 1010100101 => 8
0101001101 => 1010010110 => 7
0101001011 => 1010010101 => 7
0100110101 => 1001011010 => 6
0100101101 => 1001010110 => 6
0100101011 => 1001010101 => 6
0100011101 => 1000101110 => 6
010101010101 => 101010101010 => 12
111010010001 => 111100100010 => 12
111010000101 => 111100001010 => 12
101100100101 => 110011001010 => 12
101110010001 => 110011100010 => 11
101011010001 => 110101100010 => 12
101010010101 => 110100101010 => 12
0100000010 => 1000000100 => 9
011111000010 => 100001111100 => 7
011101101000 => 101110110000 => 9
011101100010 => 101110001100 => 9
011101001010 => 101110010100 => 10
010110110010 => 101011001100 => 9
010111101000 => 101011110000 => 8
010101101010 => 101010110100 => 9
0111010100 => 1011101000 => 8
01001010101 => 10010101010 => 7
01001001001 => 10010010010 => 8
01001001010 => 10010010100 => 9
01001000100 => 10010001000 => 11
01000100101 => 10001001010 => 8
01000100010 => 10001000100 => 9
01000101001 => 10001010010 => 8
01000101010 => 10001010100 => 8
01000100100 => 10001001000 => 10
01000010001 => 10000100010 => 9
01000010010 => 10000100100 => 9
01000010100 => 10000101000 => 9
01000001000 => 10000010000 => 10
01010010101 => 10100101010 => 8
01010001001 => 10100010010 => 10
01001000101 => 10010001010 => 9
01001000010 => 10010000100 => 10
01001010001 => 10010100010 => 9
01000100001 => 10001000010 => 10
0100000000 => 1000000000 => 10
01000000000 => 10000000000 => 11
0100000101 => 1000001010 => 8
0101010110 => 1010101001 => 9
0101011001 => 1010100110 => 8
0101011010 => 1010101100 => 7
0101100101 => 1010011010 => 7
0101100110 => 1010011001 => 8
0101101001 => 1010110010 => 8
0101101010 => 1010110100 => 8
0101101100 => 1010110001 => 7
0101110001 => 1010001110 => 7
0101110100 => 1010111000 => 7
0110010101 => 1001101010 => 6
0110010110 => 1001101001 => 7
0110011001 => 1001100110 => 6
0110011010 => 1001101100 => 7
0110100101 => 1011001010 => 9
0110100110 => 1011001001 => 8
0110101001 => 1011010010 => 9
0110101010 => 1011010100 => 9
0110101100 => 1011010001 => 8
0110110010 => 1011001100 => 8
0110110100 => 1011011000 => 8
0111000101 => 1000111010 => 6
0111001010 => 1001110100 => 7
0111001100 => 1001110001 => 7
0111010010 => 1011100100 => 8
0111011000 => 1011100001 => 7
0111100010 => 1000111100 => 6
0111100100 => 1001111000 => 7
0111101000 => 1011110000 => 7
010101011010 => 101010101100 => 8
010101101001 => 101010110010 => 9
010101110100 => 101010111000 => 8
010110100101 => 101011001010 => 10
010110101001 => 101011010010 => 10
010110101010 => 101011010100 => 10
010110110100 => 101011011000 => 8
010111010001 => 101011100010 => 9
010111010010 => 101011100100 => 9
010111010100 => 101011101000 => 9
011010010101 => 101100101010 => 11
011010011010 => 101100101100 => 10
011010100101 => 101101001010 => 11
011010101001 => 101101010010 => 11
011010101010 => 101101010100 => 11
011010110010 => 101101001100 => 10
011010110100 => 101101011000 => 10
011011001001 => 101100110010 => 10
011011001010 => 101100110100 => 10
011011010001 => 101101100010 => 10
011011010010 => 101101100100 => 10
011011010100 => 101101101000 => 10
011011100100 => 101100111000 => 9
011011101000 => 101101110000 => 8
011101000101 => 101110001010 => 10
011101001001 => 101110010010 => 10
011101010001 => 101110100010 => 10
011101010010 => 101110100100 => 10
011101010100 => 101110101000 => 10
011101100100 => 101110011000 => 9
011110100001 => 101111000010 => 9
011110100010 => 101111000100 => 9
011110100100 => 101111001000 => 9
011110101000 => 101111010000 => 9
011111010000 => 101111100000 => 8
101001110100 => 110010111000 => 11
0101111101 => 1010111110 => 5
11111111101 => 11111111110 => 11
101001010101 => 110010101010 => 12
101001101001 => 110010110010 => 12
101010100101 => 110101001010 => 12
101010101001 => 110101010010 => 12
101011001001 => 110100110010 => 12
101100101001 => 110011010010 => 11
101101000101 => 110110001010 => 12
101101001001 => 110110010010 => 12
101101010001 => 110110100010 => 12
101110100001 => 110111000010 => 11
110100010101 => 111000101010 => 12
110100100101 => 111001001010 => 12
110100101001 => 111001010010 => 12
110101000101 => 111010001010 => 12
110101001001 => 111010010010 => 12
110101010001 => 111010100010 => 12
110110001001 => 111000110010 => 12
110110010001 => 111001100010 => 12
110110100001 => 111011000010 => 12
111010001001 => 111100010010 => 12
111010100001 => 111101000010 => 12
111101000001 => 111110000010 => 12
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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:
1,3 2,2,4 3,4,3,6 6,6,6,6,8 9,11,10,11,9,14 18,18,18,18,18,18,20 30,33,30,34,30,33,30,36 56,56,58,56,56,58,56,56,60
$F_{1} = 2\ q$
$F_{2} = q + 3\ q^{2}$
$F_{3} = 2\ q + 2\ q^{2} + 4\ q^{3}$
$F_{4} = 3\ q + 4\ q^{2} + 3\ q^{3} + 6\ q^{4}$
$F_{5} = 6\ q + 6\ q^{2} + 6\ q^{3} + 6\ q^{4} + 8\ q^{5}$
$F_{6} = 9\ q + 11\ q^{2} + 10\ q^{3} + 11\ q^{4} + 9\ q^{5} + 14\ q^{6}$
$F_{7} = 18\ q + 18\ q^{2} + 18\ q^{3} + 18\ q^{4} + 18\ q^{5} + 18\ q^{6} + 20\ q^{7}$
$F_{8} = 30\ q + 33\ q^{2} + 30\ q^{3} + 34\ q^{4} + 30\ q^{5} + 33\ q^{6} + 30\ q^{7} + 36\ q^{8}$
$F_{9} = 56\ q + 56\ q^{2} + 58\ q^{3} + 56\ q^{4} + 56\ q^{5} + 58\ q^{6} + 56\ q^{7} + 56\ q^{8} + 60\ q^{9}$
Description
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rowmotion
Description
Return the rowmotion of the binary word, regarded as an order ideal in the product of two chains.
In particular, this operation preserves the number of ones, and its order is the length of the word, see section 3.3 of [1].
In particular, this operation preserves the number of ones, and its order is the length of the word, see section 3.3 of [1].
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