************************************************************************ * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2013 The FindStatCrew * * * * This information is distributed in the hope that it will be * * useful, but WITHOUT ANY WARRANTY; without even the implied * * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ************************************************************************ ------------------------------------------------------------------------ Map identifier: Mp00096 ------------------------------------------------------------------------ Map name: Foata bijection ------------------------------------------------------------------------ Domain: Binary words ------------------------------------------------------------------------ Codomain: Binary words ------------------------------------------------------------------------ Description: The Foata bijection $\phi$ is a bijection on the set of words of given content (by a slight generalization of Section 2 in [1]). Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$. At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows. * If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$. * If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$. In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right. For instance, to compute $\phi(4154223)$, the sequence of words is * 4, * |4|1 -- > 41, * |4|1|5 -- > 415, * |415|4 -- > 5414, * |5|4|14|2 -- > 54412, * |5441|2|2 -- > 154422, * |1|5442|2|3 -- > 1254423. So $\phi(4154223) = 1254423$. ------------------------------------------------------------------------ References: [1] Foata, D., Schützenberger, M.-P. Major index and inversion number of permutations [[MathSciNet:0506852]] [2] Foata bijection [[Mp00067]] ------------------------------------------------------------------------ Code: def mapping(w): return w.foata_bijection() ------------------------------------------------------------------------ Map images: 0 => 0 1 => 1 00 => 00 01 => 01 10 => 10 11 => 11 000 => 000 001 => 001 010 => 100 011 => 011 100 => 010 101 => 101 110 => 110 111 => 111 0000 => 0000 0001 => 0001 0010 => 1000 0011 => 0011 0100 => 0100 0101 => 1001 0110 => 1010 0111 => 0111 1000 => 0010 1001 => 0101 1010 => 1100 1011 => 1011 1100 => 0110 1101 => 1101 1110 => 1110 1111 => 1111 00000 => 00000 00001 => 00001 00010 => 10000 00011 => 00011 00100 => 01000 00101 => 10001 00110 => 10010 00111 => 00111 01000 => 00100 01001 => 01001 01010 => 11000 01011 => 10011 01100 => 01010 01101 => 10101 01110 => 10110 01111 => 01111 10000 => 00010 10001 => 00101 10010 => 10100 10011 => 01011 10100 => 01100 10101 => 11001 10110 => 11010 10111 => 10111 11000 => 00110 11001 => 01101 11010 => 11100 11011 => 11011 11100 => 01110 11101 => 11101 11110 => 11110 11111 => 11111 000000 => 000000 000001 => 000001 000010 => 100000 000011 => 000011 000100 => 010000 000101 => 100001 000110 => 100010 000111 => 000111 001000 => 001000 001001 => 010001 001010 => 110000 001011 => 100011 001100 => 010010 001101 => 100101 001110 => 100110 001111 => 001111 010000 => 000100 010001 => 001001 010010 => 101000 010011 => 010011 010100 => 011000 010101 => 110001 010110 => 110010 010111 => 100111 011000 => 001010 011001 => 010101 011010 => 110100 011011 => 101011 011100 => 010110 011101 => 101101 011110 => 101110 011111 => 011111 100000 => 000010 100001 => 000101 100010 => 100100 100011 => 001011 100100 => 010100 100101 => 101001 100110 => 101010 100111 => 010111 101000 => 001100 101001 => 011001 101010 => 111000 101011 => 110011 101100 => 011010 101101 => 110101 101110 => 110110 101111 => 101111 110000 => 000110 110001 => 001101 110010 => 101100 110011 => 011011 110100 => 011100 110101 => 111001 110110 => 111010 110111 => 110111 111000 => 001110 111001 => 011101 111010 => 111100 111011 => 111011 111100 => 011110 111101 => 111101 111110 => 111110 111111 => 111111 0000000 => 0000000 0000001 => 0000001 0000010 => 1000000 0000011 => 0000011 0000100 => 0100000 0000101 => 1000001 0000110 => 1000010 0000111 => 0000111 0001000 => 0010000 0001001 => 0100001 0001010 => 1100000 0001011 => 1000011 0001100 => 0100010 0001101 => 1000101 0001110 => 1000110 0001111 => 0001111 0010000 => 0001000 0010001 => 0010001 0010010 => 1010000 0010011 => 0100011 0010100 => 0110000 0010101 => 1100001 0010110 => 1100010 0010111 => 1000111 0011000 => 0010010 0011001 => 0100101 0011010 => 1100100 0011011 => 1001011 0011100 => 0100110 0011101 => 1001101 0011110 => 1001110 0011111 => 0011111 0100000 => 0000100 0100001 => 0001001 0100010 => 1001000 0100011 => 0010011 0100100 => 0101000 0100101 => 1010001 0100110 => 1010010 0100111 => 0100111 0101000 => 0011000 0101001 => 0110001 0101010 => 1110000 0101011 => 1100011 0101100 => 0110010 0101101 => 1100101 0101110 => 1100110 0101111 => 1001111 0110000 => 0001010 0110001 => 0010101 0110010 => 1010100 0110011 => 0101011 0110100 => 0110100 0110101 => 1101001 0110110 => 1101010 0110111 => 1010111 0111000 => 0010110 0111001 => 0101101 0111010 => 1101100 0111011 => 1011011 0111100 => 0101110 0111101 => 1011101 0111110 => 1011110 0111111 => 0111111 1000000 => 0000010 1000001 => 0000101 1000010 => 1000100 1000011 => 0001011 1000100 => 0100100 1000101 => 1001001 1000110 => 1001010 1000111 => 0010111 1001000 => 0010100 1001001 => 0101001 1001010 => 1101000 1001011 => 1010011 1001100 => 0101010 1001101 => 1010101 1001110 => 1010110 1001111 => 0101111 1010000 => 0001100 1010001 => 0011001 1010010 => 1011000 1010011 => 0110011 1010100 => 0111000 1010101 => 1110001 1010110 => 1110010 1010111 => 1100111 1011000 => 0011010 1011001 => 0110101 1011010 => 1110100 1011011 => 1101011 1011100 => 0110110 1011101 => 1101101 1011110 => 1101110 1011111 => 1011111 1100000 => 0000110 1100001 => 0001101 1100010 => 1001100 1100011 => 0011011 1100100 => 0101100 1100101 => 1011001 1100110 => 1011010 1100111 => 0110111 1101000 => 0011100 1101001 => 0111001 1101010 => 1111000 1101011 => 1110011 1101100 => 0111010 1101101 => 1110101 1101110 => 1110110 1101111 => 1101111 1110000 => 0001110 1110001 => 0011101 1110010 => 1011100 1110011 => 0111011 1110100 => 0111100 1110101 => 1111001 1110110 => 1111010 1110111 => 1110111 1111000 => 0011110 1111001 => 0111101 1111010 => 1111100 1111011 => 1111011 1111100 => 0111110 1111101 => 1111101 1111110 => 1111110 1111111 => 1111111 00000000 => 00000000 00000001 => 00000001 00000010 => 10000000 00000011 => 00000011 00000100 => 01000000 00000101 => 10000001 00000110 => 10000010 00000111 => 00000111 00001000 => 00100000 00001001 => 01000001 00001010 => 11000000 00001011 => 10000011 00001100 => 01000010 00001101 => 10000101 00001110 => 10000110 00001111 => 00001111 00010000 => 00010000 00010001 => 00100001 00010010 => 10100000 00010011 => 01000011 00010100 => 01100000 00010101 => 11000001 00010110 => 11000010 00010111 => 10000111 00011000 => 00100010 00011001 => 01000101 00011010 => 11000100 00011011 => 10001011 00011100 => 01000110 00011101 => 10001101 00011110 => 10001110 00011111 => 00011111 00100000 => 00001000 00100001 => 00010001 00100010 => 10010000 00100011 => 00100011 00100100 => 01010000 00100101 => 10100001 00100110 => 10100010 00100111 => 01000111 00101000 => 00110000 00101001 => 01100001 00101010 => 11100000 00101011 => 11000011 00101100 => 01100010 00101101 => 11000101 00101110 => 11000110 00101111 => 10001111 00110000 => 00010010 00110001 => 00100101 00110010 => 10100100 00110011 => 01001011 00110100 => 01100100 00110101 => 11001001 00110110 => 11001010 00110111 => 10010111 00111000 => 00100110 00111001 => 01001101 00111010 => 11001100 00111011 => 10011011 00111100 => 01001110 00111101 => 10011101 00111110 => 10011110 00111111 => 00111111 01000000 => 00000100 01000001 => 00001001 01000010 => 10001000 01000011 => 00010011 01000100 => 01001000 01000101 => 10010001 01000110 => 10010010 01000111 => 00100111 01001000 => 00101000 01001001 => 01010001 01001010 => 11010000 01001011 => 10100011 01001100 => 01010010 01001101 => 10100101 01001110 => 10100110 01001111 => 01001111 01010000 => 00011000 01010001 => 00110001 01010010 => 10110000 01010011 => 01100011 01010100 => 01110000 01010101 => 11100001 01010110 => 11100010 01010111 => 11000111 01011000 => 00110010 01011001 => 01100101 01011010 => 11100100 01011011 => 11001011 01011100 => 01100110 01011101 => 11001101 01011110 => 11001110 01011111 => 10011111 01100000 => 00001010 01100001 => 00010101 01100010 => 10010100 01100011 => 00101011 01100100 => 01010100 01100101 => 10101001 01100110 => 10101010 01100111 => 01010111 01101000 => 00110100 01101001 => 01101001 01101010 => 11101000 01101011 => 11010011 01101100 => 01101010 01101101 => 11010101 01101110 => 11010110 01101111 => 10101111 01110000 => 00010110 01110001 => 00101101 01110010 => 10101100 01110011 => 01011011 01110100 => 01101100 01110101 => 11011001 01110110 => 11011010 01110111 => 10110111 01111000 => 00101110 01111001 => 01011101 01111010 => 11011100 01111011 => 10111011 01111100 => 01011110 01111101 => 10111101 01111110 => 10111110 01111111 => 01111111 10000000 => 00000010 10000001 => 00000101 10000010 => 10000100 10000011 => 00001011 10000100 => 01000100 10000101 => 10001001 10000110 => 10001010 10000111 => 00010111 10001000 => 00100100 10001001 => 01001001 10001010 => 11001000 10001011 => 10010011 10001100 => 01001010 10001101 => 10010101 10001110 => 10010110 10001111 => 00101111 10010000 => 00010100 10010001 => 00101001 10010010 => 10101000 10010011 => 01010011 10010100 => 01101000 10010101 => 11010001 10010110 => 11010010 10010111 => 10100111 10011000 => 00101010 10011001 => 01010101 10011010 => 11010100 10011011 => 10101011 10011100 => 01010110 10011101 => 10101101 10011110 => 10101110 10011111 => 01011111 10100000 => 00001100 10100001 => 00011001 10100010 => 10011000 10100011 => 00110011 10100100 => 01011000 10100101 => 10110001 10100110 => 10110010 10100111 => 01100111 10101000 => 00111000 10101001 => 01110001 10101010 => 11110000 10101011 => 11100011 10101100 => 01110010 10101101 => 11100101 10101110 => 11100110 10101111 => 11001111 10110000 => 00011010 10110001 => 00110101 10110010 => 10110100 10110011 => 01101011 10110100 => 01110100 10110101 => 11101001 10110110 => 11101010 10110111 => 11010111 10111000 => 00110110 10111001 => 01101101 10111010 => 11101100 10111011 => 11011011 10111100 => 01101110 10111101 => 11011101 10111110 => 11011110 10111111 => 10111111 11000000 => 00000110 11000001 => 00001101 11000010 => 10001100 11000011 => 00011011 11000100 => 01001100 11000101 => 10011001 11000110 => 10011010 11000111 => 00110111 11001000 => 00101100 11001001 => 01011001 11001010 => 11011000 11001011 => 10110011 11001100 => 01011010 11001101 => 10110101 11001110 => 10110110 11001111 => 01101111 11010000 => 00011100 11010001 => 00111001 11010010 => 10111000 11010011 => 01110011 11010100 => 01111000 11010101 => 11110001 11010110 => 11110010 11010111 => 11100111 11011000 => 00111010 11011001 => 01110101 11011010 => 11110100 11011011 => 11101011 11011100 => 01110110 11011101 => 11101101 11011110 => 11101110 11011111 => 11011111 11100000 => 00001110 11100001 => 00011101 11100010 => 10011100 11100011 => 00111011 11100100 => 01011100 11100101 => 10111001 11100110 => 10111010 11100111 => 01110111 11101000 => 00111100 11101001 => 01111001 11101010 => 11111000 11101011 => 11110011 11101100 => 01111010 11101101 => 11110101 11101110 => 11110110 11101111 => 11101111 11110000 => 00011110 11110001 => 00111101 11110010 => 10111100 11110011 => 01111011 11110100 => 01111100 11110101 => 11111001 11110110 => 11111010 11110111 => 11110111 11111000 => 00111110 11111001 => 01111101 11111010 => 11111100 11111011 => 11111011 11111100 => 01111110 11111101 => 11111101 11111110 => 11111110 11111111 => 11111111 000000000 => 000000000 000000001 => 000000001 000000010 => 100000000 000000011 => 000000011 000000100 => 010000000 000000101 => 100000001 000000110 => 100000010 000000111 => 000000111 000001000 => 001000000 000001001 => 010000001 000001010 => 110000000 000001011 => 100000011 000001100 => 010000010 000001101 => 100000101 000001110 => 100000110 000001111 => 000001111 000010000 => 000100000 000010001 => 001000001 000010010 => 101000000 000010011 => 010000011 000010100 => 011000000 000010101 => 110000001 000010110 => 110000010 000010111 => 100000111 000011000 => 001000010 000011001 => 010000101 000011010 => 110000100 000011011 => 100001011 000011100 => 010000110 000011101 => 100001101 000011110 => 100001110 000011111 => 000011111 000100000 => 000010000 000100001 => 000100001 000100010 => 100100000 000100011 => 001000011 000100100 => 010100000 000100101 => 101000001 000100110 => 101000010 000100111 => 010000111 000101000 => 001100000 000101001 => 011000001 000101010 => 111000000 000101011 => 110000011 000101100 => 011000010 000101101 => 110000101 000101110 => 110000110 000101111 => 100001111 000110000 => 000100010 000110001 => 001000101 000110010 => 101000100 000110011 => 010001011 000110100 => 011000100 000110101 => 110001001 000110110 => 110001010 000110111 => 100010111 000111000 => 001000110 000111001 => 010001101 000111010 => 110001100 000111011 => 100011011 000111100 => 010001110 000111101 => 100011101 000111110 => 100011110 000111111 => 000111111 001000000 => 000001000 001000001 => 000010001 001000010 => 100010000 001000011 => 000100011 001000100 => 010010000 001000101 => 100100001 001000110 => 100100010 001000111 => 001000111 001001000 => 001010000 001001001 => 010100001 001001010 => 110100000 001001011 => 101000011 001001100 => 010100010 001001101 => 101000101 001001110 => 101000110 001001111 => 010001111 001010000 => 000110000 001010001 => 001100001 001010010 => 101100000 001010011 => 011000011 001010100 => 011100000 001010101 => 111000001 001010110 => 111000010 001010111 => 110000111 001011000 => 001100010 001011001 => 011000101 001011010 => 111000100 001011011 => 110001011 001011100 => 011000110 001011101 => 110001101 001011110 => 110001110 001011111 => 100011111 001100000 => 000010010 001100001 => 000100101 001100010 => 100100100 001100011 => 001001011 001100100 => 010100100 001100101 => 101001001 001100110 => 101001010 001100111 => 010010111 001101000 => 001100100 001101001 => 011001001 001101010 => 111001000 001101011 => 110010011 001101100 => 011001010 001101101 => 110010101 001101110 => 110010110 001101111 => 100101111 001110000 => 000100110 001110001 => 001001101 001110010 => 101001100 001110011 => 010011011 001110100 => 011001100 001110101 => 110011001 001110110 => 110011010 001110111 => 100110111 001111000 => 001001110 001111001 => 010011101 001111010 => 110011100 001111011 => 100111011 001111100 => 010011110 001111101 => 100111101 001111110 => 100111110 001111111 => 001111111 010000000 => 000000100 010000001 => 000001001 010000010 => 100001000 010000011 => 000010011 010000100 => 010001000 010000101 => 100010001 010000110 => 100010010 010000111 => 000100111 010001000 => 001001000 010001001 => 010010001 010001010 => 110010000 010001011 => 100100011 010001100 => 010010010 010001101 => 100100101 010001110 => 100100110 010001111 => 001001111 010010000 => 000101000 010010001 => 001010001 010010010 => 101010000 010010011 => 010100011 010010100 => 011010000 010010101 => 110100001 010010110 => 110100010 010010111 => 101000111 010011000 => 001010010 010011001 => 010100101 010011010 => 110100100 010011011 => 101001011 010011100 => 010100110 010011101 => 101001101 010011110 => 101001110 010011111 => 010011111 010100000 => 000011000 010100001 => 000110001 010100010 => 100110000 010100011 => 001100011 010100100 => 010110000 010100101 => 101100001 010100110 => 101100010 010100111 => 011000111 010101000 => 001110000 010101001 => 011100001 010101010 => 111100000 010101011 => 111000011 010101100 => 011100010 010101101 => 111000101 010101110 => 111000110 010101111 => 110001111 010110000 => 000110010 010110001 => 001100101 010110010 => 101100100 010110011 => 011001011 010110100 => 011100100 010110101 => 111001001 010110110 => 111001010 010110111 => 110010111 010111000 => 001100110 010111001 => 011001101 010111010 => 111001100 010111011 => 110011011 010111100 => 011001110 010111101 => 110011101 010111110 => 110011110 010111111 => 100111111 011000000 => 000001010 011000001 => 000010101 011000010 => 100010100 011000011 => 000101011 011000100 => 010010100 011000101 => 100101001 011000110 => 100101010 011000111 => 001010111 011001000 => 001010100 011001001 => 010101001 011001010 => 110101000 011001011 => 101010011 011001100 => 010101010 011001101 => 101010101 011001110 => 101010110 011001111 => 010101111 011010000 => 000110100 011010001 => 001101001 011010010 => 101101000 011010011 => 011010011 011010100 => 011101000 011010101 => 111010001 011010110 => 111010010 011010111 => 110100111 011011000 => 001101010 011011001 => 011010101 011011010 => 111010100 011011011 => 110101011 011011100 => 011010110 011011101 => 110101101 011011110 => 110101110 011011111 => 101011111 011100000 => 000010110 011100001 => 000101101 011100010 => 100101100 011100011 => 001011011 011100100 => 010101100 011100101 => 101011001 011100110 => 101011010 011100111 => 010110111 011101000 => 001101100 011101001 => 011011001 011101010 => 111011000 011101011 => 110110011 011101100 => 011011010 011101101 => 110110101 011101110 => 110110110 011101111 => 101101111 011110000 => 000101110 011110001 => 001011101 011110010 => 101011100 011110011 => 010111011 011110100 => 011011100 011110101 => 110111001 011110110 => 110111010 011110111 => 101110111 011111000 => 001011110 011111001 => 010111101 011111010 => 110111100 011111011 => 101111011 011111100 => 010111110 011111101 => 101111101 011111110 => 101111110 011111111 => 011111111 100000000 => 000000010 100000001 => 000000101 100000010 => 100000100 100000011 => 000001011 100000100 => 010000100 100000101 => 100001001 100000110 => 100001010 100000111 => 000010111 100001000 => 001000100 100001001 => 010001001 100001010 => 110001000 100001011 => 100010011 100001100 => 010001010 100001101 => 100010101 100001110 => 100010110 100001111 => 000101111 100010000 => 000100100 100010001 => 001001001 100010010 => 101001000 100010011 => 010010011 100010100 => 011001000 100010101 => 110010001 100010110 => 110010010 100010111 => 100100111 100011000 => 001001010 100011001 => 010010101 100011010 => 110010100 100011011 => 100101011 100011100 => 010010110 100011101 => 100101101 100011110 => 100101110 100011111 => 001011111 100100000 => 000010100 100100001 => 000101001 100100010 => 100101000 100100011 => 001010011 100100100 => 010101000 100100101 => 101010001 100100110 => 101010010 100100111 => 010100111 100101000 => 001101000 100101001 => 011010001 100101010 => 111010000 100101011 => 110100011 100101100 => 011010010 100101101 => 110100101 100101110 => 110100110 100101111 => 101001111 100110000 => 000101010 100110001 => 001010101 100110010 => 101010100 100110011 => 010101011 100110100 => 011010100 100110101 => 110101001 100110110 => 110101010 100110111 => 101010111 100111000 => 001010110 100111001 => 010101101 100111010 => 110101100 100111011 => 101011011 100111100 => 010101110 100111101 => 101011101 100111110 => 101011110 100111111 => 010111111 101000000 => 000001100 101000001 => 000011001 101000010 => 100011000 101000011 => 000110011 101000100 => 010011000 101000101 => 100110001 101000110 => 100110010 101000111 => 001100111 101001000 => 001011000 101001001 => 010110001 101001010 => 110110000 101001011 => 101100011 101001100 => 010110010 101001101 => 101100101 101001110 => 101100110 101001111 => 011001111 101010000 => 000111000 101010001 => 001110001 101010010 => 101110000 101010011 => 011100011 101010100 => 011110000 101010101 => 111100001 101010110 => 111100010 101010111 => 111000111 101011000 => 001110010 101011001 => 011100101 101011010 => 111100100 101011011 => 111001011 101011100 => 011100110 101011101 => 111001101 101011110 => 111001110 101011111 => 110011111 101100000 => 000011010 101100001 => 000110101 101100010 => 100110100 101100011 => 001101011 101100100 => 010110100 101100101 => 101101001 101100110 => 101101010 101100111 => 011010111 101101000 => 001110100 101101001 => 011101001 101101010 => 111101000 101101011 => 111010011 101101100 => 011101010 101101101 => 111010101 101101110 => 111010110 101101111 => 110101111 101110000 => 000110110 101110001 => 001101101 101110010 => 101101100 101110011 => 011011011 101110100 => 011101100 101110101 => 111011001 101110110 => 111011010 101110111 => 110110111 101111000 => 001101110 101111001 => 011011101 101111010 => 111011100 101111011 => 110111011 101111100 => 011011110 101111101 => 110111101 101111110 => 110111110 101111111 => 101111111 110000000 => 000000110 110000001 => 000001101 110000010 => 100001100 110000011 => 000011011 110000100 => 010001100 110000101 => 100011001 110000110 => 100011010 110000111 => 000110111 110001000 => 001001100 110001001 => 010011001 110001010 => 110011000 110001011 => 100110011 110001100 => 010011010 110001101 => 100110101 110001110 => 100110110 110001111 => 001101111 110010000 => 000101100 110010001 => 001011001 110010010 => 101011000 110010011 => 010110011 110010100 => 011011000 110010101 => 110110001 110010110 => 110110010 110010111 => 101100111 110011000 => 001011010 110011001 => 010110101 110011010 => 110110100 110011011 => 101101011 110011100 => 010110110 110011101 => 101101101 110011110 => 101101110 110011111 => 011011111 110100000 => 000011100 110100001 => 000111001 110100010 => 100111000 110100011 => 001110011 110100100 => 010111000 110100101 => 101110001 110100110 => 101110010 110100111 => 011100111 110101000 => 001111000 110101001 => 011110001 110101010 => 111110000 110101011 => 111100011 110101100 => 011110010 110101101 => 111100101 110101110 => 111100110 110101111 => 111001111 110110000 => 000111010 110110001 => 001110101 110110010 => 101110100 110110011 => 011101011 110110100 => 011110100 110110101 => 111101001 110110110 => 111101010 110110111 => 111010111 110111000 => 001110110 110111001 => 011101101 110111010 => 111101100 110111011 => 111011011 110111100 => 011101110 110111101 => 111011101 110111110 => 111011110 110111111 => 110111111 111000000 => 000001110 111000001 => 000011101 111000010 => 100011100 111000011 => 000111011 111000100 => 010011100 111000101 => 100111001 111000110 => 100111010 111000111 => 001110111 111001000 => 001011100 111001001 => 010111001 111001010 => 110111000 111001011 => 101110011 111001100 => 010111010 111001101 => 101110101 111001110 => 101110110 111001111 => 011101111 111010000 => 000111100 111010001 => 001111001 111010010 => 101111000 111010011 => 011110011 111010100 => 011111000 111010101 => 111110001 111010110 => 111110010 111010111 => 111100111 111011000 => 001111010 111011001 => 011110101 111011010 => 111110100 111011011 => 111101011 111011100 => 011110110 111011101 => 111101101 111011110 => 111101110 111011111 => 111011111 111100000 => 000011110 111100001 => 000111101 111100010 => 100111100 111100011 => 001111011 111100100 => 010111100 111100101 => 101111001 111100110 => 101111010 111100111 => 011110111 111101000 => 001111100 111101001 => 011111001 111101010 => 111111000 111101011 => 111110011 111101100 => 011111010 111101101 => 111110101 111101110 => 111110110 111101111 => 111101111 111110000 => 000111110 111110001 => 001111101 111110010 => 101111100 111110011 => 011111011 111110100 => 011111100 111110101 => 111111001 111110110 => 111111010 111110111 => 111110111 111111000 => 001111110 111111001 => 011111101 111111010 => 111111100 111111011 => 111111011 111111100 => 011111110 111111101 => 111111101 111111110 => 111111110 111111111 => 111111111 1010101010 => 1111100000 1010101100 => 0111100010 1010110010 => 1011100100 1010110100 => 0111100100 1010111000 => 0011100110 1011001010 => 1101101000 1011001100 => 0101101010 1011010010 => 1011101000 1011010100 => 0111101000 1011011000 => 0011101010 1011100010 => 1001101100 1011100100 => 0101101100 1011101000 => 0011101100 1011110000 => 0001101110 1100101010 => 1110110000 1100101100 => 0110110010 1100110010 => 1010110100 1100110100 => 0110110100 1100111000 => 0010110110 1101001010 => 1101110000 1101001100 => 0101110010 1101010010 => 1011110000 1101010100 => 0111110000 1101011000 => 0011110010 1101100010 => 1001110100 1101100100 => 0101110100 1101101000 => 0011110100 1101110000 => 0001110110 1110001010 => 1100111000 1110001100 => 0100111010 1110010010 => 1010111000 1110010100 => 0110111000 1110011000 => 0010111010 1110100010 => 1001111000 1110100100 => 0101111000 1110101000 => 0011111000 1110110000 => 0001111010 1111000010 => 1000111100 1111000100 => 0100111100 1111001000 => 0010111100 1111010000 => 0001111100 1111100000 => 0000111110 101010101010 => 111111000000 101010101100 => 011111000010 101010110010 => 101111000100 101010110100 => 011111000100 101010111000 => 001111000110 101011001010 => 110111001000 101011001100 => 010111001010 101011010010 => 101111001000 101011010100 => 011111001000 101011011000 => 001111001010 101011100010 => 100111001100 101011100100 => 010111001100 101011101000 => 001111001100 101011110000 => 000111001110 101100101010 => 111011010000 101100101100 => 011011010010 101100110010 => 101011010100 101100110100 => 011011010100 101100111000 => 001011010110 101101001010 => 110111010000 101101001100 => 010111010010 101101010010 => 101111010000 101101010100 => 011111010000 101101011000 => 001111010010 101101100010 => 100111010100 101101100100 => 010111010100 101101101000 => 001111010100 101101110000 => 000111010110 101110001010 => 110011011000 101110001100 => 010011011010 101110010010 => 101011011000 101110010100 => 011011011000 101110011000 => 001011011010 101110100010 => 100111011000 101110100100 => 010111011000 101110101000 => 001111011000 101110110000 => 000111011010 101111000010 => 100011011100 101111000100 => 010011011100 101111001000 => 001011011100 101111010000 => 000111011100 101111100000 => 000011011110 110010101010 => 111101100000 110010101100 => 011101100010 110010110010 => 101101100100 110010110100 => 011101100100 110010111000 => 001101100110 110011001010 => 110101101000 110011001100 => 010101101010 110011010010 => 101101101000 110011010100 => 011101101000 110011011000 => 001101101010 110011100010 => 100101101100 110011100100 => 010101101100 110011101000 => 001101101100 110011110000 => 000101101110 110100101010 => 111011100000 110100101100 => 011011100010 110100110010 => 101011100100 110100110100 => 011011100100 110100111000 => 001011100110 110101001010 => 110111100000 110101001100 => 010111100010 110101010010 => 101111100000 110101010100 => 011111100000 110101011000 => 001111100010 110101100010 => 100111100100 110101100100 => 010111100100 110101101000 => 001111100100 110101110000 => 000111100110 110110001010 => 110011101000 110110001100 => 010011101010 110110010010 => 101011101000 110110010100 => 011011101000 110110011000 => 001011101010 110110100010 => 100111101000 110110100100 => 010111101000 110110101000 => 001111101000 110110110000 => 000111101010 110111000010 => 100011101100 110111000100 => 010011101100 110111001000 => 001011101100 110111010000 => 000111101100 110111100000 => 000011101110 111000101010 => 111001110000 111000101100 => 011001110010 111000110010 => 101001110100 111000110100 => 011001110100 111000111000 => 001001110110 111001001010 => 110101110000 111001001100 => 010101110010 111001010010 => 101101110000 111001010100 => 011101110000 111001011000 => 001101110010 111001100010 => 100101110100 111001100100 => 010101110100 111001101000 => 001101110100 111001110000 => 000101110110 111010001010 => 110011110000 111010001100 => 010011110010 111010010010 => 101011110000 111010010100 => 011011110000 111010011000 => 001011110010 111010100010 => 100111110000 111010100100 => 010111110000 111010101000 => 001111110000 111010110000 => 000111110010 111011000010 => 100011110100 111011000100 => 010011110100 111011001000 => 001011110100 111011010000 => 000111110100 111011100000 => 000011110110 111100001010 => 110001111000 111100001100 => 010001111010 111100010010 => 101001111000 111100010100 => 011001111000 111100011000 => 001001111010 111100100010 => 100101111000 111100100100 => 010101111000 111100101000 => 001101111000 111100110000 => 000101111010 111101000010 => 100011111000 111101000100 => 010011111000 111101001000 => 001011111000 111101010000 => 000111111000 111101100000 => 000011111010 111110000010 => 100001111100 111110000100 => 010001111100 111110001000 => 001001111100 111110010000 => 000101111100 111110100000 => 000011111100 111111000000 => 000001111110 10101010101010 => 11111110000000 10101010101100 => 01111110000010 10101010110010 => 10111110000100 10101010110100 => 01111110000100 ----------------------------------------------------------------------------- Created: Jan 29, 2020 at 13:26 by FindStatCrew ----------------------------------------------------------------------------- Last Updated: Jan 29, 2020 at 13:26 by Martin Rubey