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Identifier
Mp00280: Binary words path rowmotionBinary words
Images
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000111111110=>001011111111 000111110010=>001001111101 000111001000=>001001110001 000111001110=>001001110111 000111000010=>001000011101 000111011010=>001011101101 000100100000=>001001000001 000100100110=>001001001011 000100111000=>001001000111 000100111110=>001001011111 000100110010=>001001001101 000100001000=>001000010001 000100001110=>001000010111 000100000010=>001000000101 000100011010=>001000101101 000101101000=>001010110001 000101101110=>001010110111 000101100010=>001010001101 000101111010=>001010111101 000101001010=>001010010101 011000000000=>100000000011 011000000110=>100000011011 011000011000=>100001100011 011000011110=>100001101111 011000010010=>100001100101 011001100000=>100110000011 011001100110=>100110011011 011001111000=>100110001111 011001111110=>100110111111 011001110010=>100110011101 011001001000=>100110010001 011001001110=>100110010111 011001000010=>100110000101 011001011010=>100110101101 011110000000=>100000001111 011110000110=>100001111011 011110011000=>100111100011 011110011110=>100111101111 011110010010=>100111100101 011111100000=>100000111111 011111100110=>100111111011 011111111000=>100011111111 011111111110=>101111111111 011111110010=>100111111101 011111001000=>100111110001 011111001110=>100111110111 011111000010=>100001111101 011111011010=>101111101101 011100100000=>100111000001 011100100110=>100111001011 011100111000=>100111000111 011100111110=>100111011111 011100110010=>100111001101 011100001000=>100001110001 011100001110=>100001110111 011100000010=>100000011101 011100011010=>100011101101 011101101000=>101110110001 011101101110=>101110110111 011101100010=>101110001101 011101111010=>101110111101 011101001010=>101110010101 010010000000=>100100000001 010010000110=>100100001011 010010011000=>100100100011 010010011110=>100100101111 010010010010=>100100100101 010011100000=>100100000111 010011100110=>100100111011 010011111000=>100100011111 010011111110=>100101111111 010011110010=>100100111101 010011001000=>100100110001 010011001110=>100100110111 010011000010=>100100001101 010011011010=>100101101101 010000100000=>100001000001 010000100110=>100001001011 010000111000=>100001000111 010000111110=>100001011111 010000110010=>100001001101 010000001000=>100000010001 010000001110=>100000010111 010000000010=>100000000101 010000011010=>100000101101 010001101000=>100010110001 010001101110=>100010110111 010001100010=>100010001101 010001111010=>100010111101 010001001010=>100010010101 010110100000=>101011000001 010110100110=>101011001011 010110111000=>101011000111 010110111110=>101011011111 010110110010=>101011001101 010110001000=>101000110001 010110001110=>101000110111 010110000010=>101000001101 010110011010=>101001101101 010111101000=>101011110001 010111101110=>101011110111 010111100010=>101000111101 010111111010=>101011111101 010111001010=>101001110101 010100101000=>101001010001 010100101110=>101001010111 010100100010=>101001000101 010100111010=>101001011101 010100001010=>101000010101 010101101010=>101010110101 001010101010=>010101010101 001010101100=>010101010011 001010110010=>010101001101 001010110100=>010101011001 001010111000=>010101000111 001011001010=>010100110101 001011001100=>010100110011 001011010010=>010101100101 001011010100=>010101101001 001011011000=>010101100011 001011100010=>010100011101 001011100100=>010100111001 001011101000=>010101110001 001011110000=>010100001111 001100101010=>010011010101 001100101100=>010011010011 001100110010=>010011001101 001100110100=>010011011001 001100111000=>010011000111 001101001010=>010110010101 001101001100=>010110010011 001101010010=>010110100101 001101010100=>010110101001 001101011000=>010110100011 001101100010=>010110001101 001101100100=>010110011001 001101101000=>010110110001 001101110000=>010110000111 001110001010=>010001110101 001110001100=>010001110011 001110010010=>010011100101 001110010100=>010011101001 001110011000=>010011100011 001110100010=>010111000101 001110100100=>010111001001 001110101000=>010111010001 001110110000=>010111000011 001111000010=>010000111101 001111000100=>010001111001 001111001000=>010011110001 001111010000=>010111100001 001111100000=>010000011111 010010101010=>100101010101 010010101100=>100101010011 010010110010=>100101001101 010010110100=>100101011001 010010111000=>100101000111 010011001010=>100100110101 010011001100=>100100110011 010011010010=>100101100101 010011010100=>100101101001 010011011000=>100101100011 010011100010=>100100011101 010011100100=>100100111001 010011101000=>100101110001 010011110000=>100100001111 010100101010=>101001010101 010100101100=>101001010011 010100110010=>101001001101 010100110100=>101001011001 010100111000=>101001000111 010101001010=>101010010101 010101001100=>101010010011 010101010010=>101010100101 010101010100=>101010101001 010101011000=>101010100011 010101100010=>101010001101 010101100100=>101010011001 010101101000=>101010110001 010101110000=>101010000111 010110001010=>101000110101 010110001100=>101000110011 010110010010=>101001100101 010110010100=>101001101001 010110011000=>101001100011 010110100010=>101011000101 010110100100=>101011001001 010110101000=>101011010001 010110110000=>101011000011 010111000010=>101000011101 010111000100=>101000111001 010111001000=>101001110001 010111010000=>101011100001 010111100000=>101000001111 011000101010=>100011010101 011000101100=>100011010011 011000110010=>100011001101 011000110100=>100011011001 011000111000=>100011000111 011001001010=>100110010101 011001001100=>100110010011 011001010010=>100110100101 011001010100=>100110101001 011001011000=>100110100011 011001100010=>100110001101 011001100100=>100110011001 011001101000=>100110110001 011001110000=>100110000111 011010001010=>101100010101 011010001100=>101100010011 011010010010=>101100100101 011010010100=>101100101001 011010011000=>101100100011 011010100010=>101101000101 011010100100=>101101001001 011010101000=>101101010001 011010110000=>101101000011 011011000010=>101100001101 011011000100=>101100011001 011011001000=>101100110001 011011010000=>101101100001 011011100000=>101100000111 011100001010=>100001110101 011100001100=>100001110011 011100010010=>100011100101 011100010100=>100011101001 011100011000=>100011100011 011100100010=>100111000101 011100100100=>100111001001 011100101000=>100111010001 011100110000=>100111000011 011101000010=>101110000101 011101000100=>101110001001 011101001000=>101110010001 011101010000=>101110100001 011101100000=>101110000011 011110000010=>100000111101 011110000100=>100001111001 011110001000=>100011110001 011110010000=>100111100001 011110100000=>101111000001 011111000000=>100000011111 010101010110=>101010101011 010101011001=>101010100110 010101011010=>101010101101 010101011100=>101010100111 010101100101=>101010011010 010101100110=>101010011011 010101101001=>101010110010 010101101100=>101010110011 010101110001=>101010001110 010101110010=>101010011101 010101110100=>101010111001 010101111000=>101010001111 010110010101=>101001101010 010110010110=>101001101011 010110011001=>101001100110 010110011100=>101001100111 010110100101=>101011001010 010110101001=>101011010010 010110101010=>101011010101 010110101100=>101011010011 010110110001=>101011000110 010110110100=>101011011001 010111000101=>101000111010 010111000110=>101000111011 010111001001=>101001110010 010111001100=>101001110011 010111010001=>101011100010 010111010010=>101011100101 010111010100=>101011101001 010111011000=>101011100011 010111100001=>101000011110 010111100100=>101001111001 010111110000=>101000011111 011001010101=>100110101010 011001010110=>100110101011 011001011001=>100110100110 011001011100=>100110100111 011001100101=>100110011010 011001101001=>100110110010 011001101010=>100110110101 011001101100=>100110110011 011001110001=>100110001110 011001110100=>100110111001 011010010101=>101100101010 011010010110=>101100101011 011010011001=>101100100110 011010011010=>101100101101 011010011100=>101100100111 011010100101=>101101001010 011010100110=>101101001011 011010101001=>101101010010 011010101010=>101101010101 011010101100=>101101010011 011010110001=>101101000110 011010110010=>101101001101 011010110100=>101101011001 011010111000=>101101000111 011011000101=>101100011010 011011000110=>101100011011 011011001001=>101100110010 011011001010=>101100110101 011011001100=>101100110011 011011010001=>101101100010 011011010010=>101101100101 011011010100=>101101101001 011011011000=>101101100011 011011100001=>101100001110 011011100010=>101100011101 011011100100=>101100111001 011011101000=>101101110001 011011110000=>101100001111 011100010101=>100011101010 011100010110=>100011101011 011100011001=>100011100110 011100011100=>100011100111 011100100101=>100111001010 011100101001=>100111010010 011100101010=>100111010101 011100101100=>100111010011 011100110001=>100111000110 011100110100=>100111011001 011101000101=>101110001010 011101000110=>101110001011 011101001001=>101110010010 011101001100=>101110010011 011101010001=>101110100010 011101010010=>101110100101 011101010100=>101110101001 011101011000=>101110100011 011101100001=>101110000110 011101100100=>101110011001 011101110000=>101110000111 011110000101=>100001111010 011110001001=>100011110010 011110001010=>100011110101 011110001100=>100011110011 011110010001=>100111100010 011110010100=>100111101001 011110100001=>101111000010 011110100010=>101111000101 011110100100=>101111001001 011110101000=>101111010001 011110110000=>101111000011 011111000001=>100000111110 011111000100=>100011111001 011111010000=>101111100001 001111000110=>010001111011 001111001010=>010011110101 100111001100=>011001110011 001111001100=>010011110011 001011010110=>010101101011 001111010010=>010111100101 100111010100=>011011101001 001111010100=>010111101001 000111010110=>001011101011 001011011010=>010101101101 100111011000=>011011100011 001111011000=>010111100011 100011011100=>001101100111 010011011100=>100101100111 001011011100=>010101100111 000111011100=>001011100111 000011011110=>000101101111 001101100110=>010110011011 001101101010=>010110110101 100101101100=>011010110011 001101101100=>010110110011 001011100110=>010100111011 001111100010=>010001111101 100111100100=>011001111001 001111100100=>010011111001 010011101010=>100101110101 001011101010=>010101110101 100111101000=>011011110001 001111101000=>010111110001 000111101010=>001011110101 100011101100=>001101110011 010011101100=>100101110011 001011101100=>010101110011 000111101100=>001011110011 000011101110=>000101110111 101001110100=>110010111001 001001110110=>010010111011 001101110010=>010110011101 100101110100=>011010111001 001101110100=>010110111001 000101110110=>001010111011 001011110010=>010100111101 100111110000=>011000011111 001111110000=>010000111111 100011110100=>001101111001 010011110100=>100101111001 001011110100=>010101111001 000111110100=>001011111001 000011110110=>000101111011 110001111000=>001110001111 101001111000=>110010001111 001001111010=>010010111101 100101111000=>011010001111 001101111000=>010110001111 100011111000=>001100011111 001011111000=>010100011111 000011111010=>000101111101 010001111100=>100010011111 001001111100=>010010011111 000101111100=>001010011111 000011111100=>000100111111 100101010101=>011010101010 100101011001=>011010100110 100101100101=>011010011010 100101101001=>011010110010 100101110001=>011010001110 100110010101=>011001101010 100110101001=>011011010010 100111000101=>011000111010 100111001001=>011001110010 100111010001=>011011100010 101001010101=>110010101010 101001101001=>110010110010 101010011001=>110100100110 101010100101=>110101001010 101010101001=>110101010010 101010110001=>110101000110 101011001001=>110100110010 101011100001=>110100001110 101100010101=>110001101010 101100101001=>110011010010 101101000101=>110110001010 101101001001=>110110010010 101101010001=>110110100010 101110001001=>110001110010 101110100001=>110111000010 110001010101=>001110101010 110001011001=>001110100110 110001100101=>001110011010 110001101001=>001110110010 110001110001=>001110001110 110010010101=>011100101010 110010011001=>011100100110 110010100101=>011101001010 110010101001=>011101010010 110010110001=>011101000110 110011000101=>011100011010 110011001001=>011100110010 110011010001=>011101100010 110011100001=>011100001110 110100010101=>111000101010 110100011001=>111000100110 110100100101=>111001001010 110100101001=>111001010010 110100110001=>111001000110 110101000101=>111010001010 110101001001=>111010010010 110101010001=>111010100010 110101100001=>111010000110 110110000101=>111000011010 110110001001=>111000110010 110110010001=>111001100010 110110100001=>111011000010 110111000001=>111000001110 111000010101=>000111101010 111000101001=>001111010010 111001000101=>011110001010 111001001001=>011110010010 111001010001=>011110100010 111010001001=>111100010010 111010100001=>111101000010 111100000101=>000011111010 111100001001=>000111110010 111100010001=>001111100010 111100100001=>011111000010 111101000001=>111110000010 10101010101010=>11010101010101 10101010101100=>11010101010011 10101010110100=>11010101011001 10101010111000=>11010101000111 10101011010100=>11010101101001 10101011100100=>11010100111001 10101011101000=>11010101110001 10101011110000=>11010100001111 10101101010100=>11010110101001 10101110010100=>11010011101001 10101110100100=>11010111001001 10101110101000=>11010111010001 10101110110000=>11010111000011 10101111000100=>11010001111001 10101111010000=>11010111100001 10110101010100=>11011010101001 10110111100000=>11011000001111 10111001010100=>11001110101001 10111010010100=>11011100101001 10111010100100=>11011101001001 10111011000100=>11011100011001 10111011010000=>11011101100001 10111011100000=>11011100000111 10111100010100=>11000111101001 10111100110000=>11001111000011 10111101000100=>11011110001001 10111101001000=>11011110010001 10111101010000=>11011110100001 10111101100000=>11011110000011 10111110000100=>11000011111001 10111110001000=>11000111110001 10111110010000=>11001111100001 10111110100000=>11011111000001 10111111000000=>11000000111111 11001111100000=>01110000011111 11010101010100=>11101010101001 11010101011000=>11101010100011 11010101100100=>11101010011001 11010101101000=>11101010110001 11010101110000=>11101010000111 11010110010100=>11101001101001 11010110011000=>11101001100011 11010110100100=>11101011001001 11010110101000=>11101011010001 11010110110000=>11101011000011 11010111000100=>11101000111001 11010111001000=>11101001110001 11010111010000=>11101011100001 11010111100000=>11101000001111 11011001010100=>11100110101001 11011001011000=>11100110100011 11011001100100=>11100110011001 11011001101000=>11100110110001 11011001110000=>11100110000111 11011010010100=>11101100101001 11011010011000=>11101100100011 11011010100100=>11101101001001 11011010101000=>11101101010001 11011010110000=>11101101000011 11011011000100=>11101100011001 11011011001000=>11101100110001 11011011010000=>11101101100001 11011011100000=>11101100000111 11011100010100=>11100011101001 11011100011000=>11100011100011 11011100100100=>11100111001001 11011100101000=>11100111010001 11011100110000=>11100111000011 11011101000100=>11101110001001 11011101001000=>11101110010001 11011101010000=>11101110100001 11011101100000=>11101110000011 11011110000010=>11100000111101 11011110000100=>11100001111001 11011110001000=>11100011110001 11011110010000=>11100111100001 11011110100000=>11101111000001 11011111000000=>11100000011111 11100101010100=>01111010101001 11100101011000=>01111010100011 11100101100100=>01111010011001 11100101101000=>01111010110001 11100101110000=>01111010000111 11100110010100=>01111001101001 11100110011000=>01111001100011 11100110100100=>01111011001001 11100110101000=>01111011010001 11100110110000=>01111011000011 11100111000100=>01111000111001 11100111001000=>01111001110001 11100111010000=>01111011100001 11100111100000=>01111000001111 11101001010100=>11110010101001 11101001011000=>11110010100011 11101001100100=>11110010011001 11101001101000=>11110010110001 11101001110000=>11110010000111 11101010010100=>11110100101001 11101010011000=>11110100100011 11101010100100=>11110101001001 11101010101000=>11110101010001 11101010110000=>11110101000011 11101011000100=>11110100011001 11101011001000=>11110100110001 11101011010000=>11110101100001 11101011100000=>11110100000111 11101100010100=>11110001101001 11101100011000=>11110001100011 11101100100100=>11110011001001 11101100101000=>11110011010001 11101100110000=>11110011000011 11101101000010=>11110110000101 11101101000100=>11110110001001 11101101001000=>11110110010001 11101101010000=>11110110100001 11101101100000=>11110110000011 11101110000010=>11110000011101 11101110000100=>11110000111001 11101110001000=>11110001110001 11101110010000=>11110011100001 11101110100000=>11110111000001 11101111000000=>11110000001111 11110001010100=>00111110101001 11110001011000=>00111110100011 11110001100100=>00111110011001 11110001101000=>00111110110001 11110001110000=>00111110000111 11110010010100=>01111100101001 11110010011000=>01111100100011 11110010100100=>01111101001001 11110010101000=>01111101010001 11110010110000=>01111101000011 11110011000010=>01111100001101 11110011000100=>01111100011001 11110011001000=>01111100110001 11110011010000=>01111101100001 11110011100000=>01111100000111 11110100010100=>11111000101001 11110100011000=>11111000100011 11110100100010=>11111001000101 11110100100100=>11111001001001 11110100101000=>11111001010001 11110100110000=>11111001000011 11110101000010=>11111010000101 11110101000100=>11111010001001 11110101001000=>11111010010001 11110101010000=>11111010100001 11110101100000=>11111010000011 11110110000010=>11111000001101 11110110000100=>11111000011001 11110110001000=>11111000110001 11110110010000=>11111001100001 11110110100000=>11111011000001 11110111000000=>11111000000111 11111000001100=>00001111110011 11111000010010=>00011111100101 11111000010100=>00011111101001 11111000011000=>00011111100011 11111000100010=>00111111000101 11111000100100=>00111111001001 11111000101000=>00111111010001 11111000110000=>00111111000011 11111001000010=>01111110000101 11111001000100=>01111110001001 11111001001000=>01111110010001 11111001010000=>01111110100001 11111001100000=>01111110000011 11111010000010=>11111100000101 11111010000100=>11111100001001 11111010001000=>11111100010001 11111010010000=>11111100100001 11111010100000=>11111101000001 11111011000000=>11111100000011 11111100000010=>00000111111101 11111100000100=>00001111111001 11111100001000=>00011111110001 11111100010000=>00111111100001 11111100100000=>01111111000001 11111101000000=>11111110000001 11111110000000=>00000011111111 1010101010101010=>1101010101010101 1010101010101100=>1101010101010011 1010101010110100=>1101010101011001 1010101010111000=>1101010101000111 1010101011010100=>1101010101101001 1010101011100100=>1101010100111001 1010101011101000=>1101010101110001 1010101011110000=>1101010100001111 1010101101010100=>1101010110101001 1010101110010100=>1101010011101001 1010101110100100=>1101010111001001 1010101111000100=>1101010001111001 1010110101010100=>1101011010101001 1010111001010100=>1101001110101001 1010111010010100=>1101011100101001 1010111100010100=>1101000111101001 1011010101010100=>1101101010101001 1011100101010100=>1100111010101001 1011101001010100=>1101110010101001 1011110001010100=>1100011110101001 1011110111000000=>1101111000000111 1011111010100000=>1101111101000001 1011111011000000=>1101111100000011 1011111100010000=>1100011111100001 1011111100100000=>1100111111000001 1011111101000000=>1101111110000001 1011111110000000=>1100000001111111 1101010101010100=>1110101010101001 1110010101010100=>0111101010101001 1110100101010100=>1111001010101001 1111000101010100=>0011111010101001 1111011100000010=>1111100000011101 1111101010000010=>1111110100000101 1111101100000010=>1111110000001101 1111110001000010=>0011111110000101 1111110010000010=>0111111100000101 1111110100000010=>1111111000000101 1111111000000010=>0000001111111101 101010101010101010=>110101010101010101 101010101010101100=>110101010101010011 101010101010110100=>110101010101011001 101010101011010100=>110101010101101001 101010101101010100=>110101010110101001 101010110101010100=>110101011010101001 101011010101010100=>110101101010101001 101101010101010100=>110110101010101001 110101010101010100=>111010101010101001 101010101010111000=>110101010101000111 101010101011100100=>110101010100111001 101010101110010100=>110101010011101001 101010111001010100=>110101001110101001 101011100101010100=>110100111010101001 101110010101010100=>110011101010101001 111001010101010100=>011110101010101001 111111110000000010=>000000011111111101 101111111100000000=>110000000011111111 111111101000000010=>111111110000000101 101111111010000000=>110111111100000001 111111100100000010=>011111111000000101 111111011000000010=>111111100000001101 101111111001000000=>110011111110000001 101111110110000000=>110111111000000011 10101010101010101010=>11010101010101010101 10101010101010101100=>11010101010101010011 10101010101010110100=>11010101010101011001 10101010101011010100=>11010101010101101001 10101010101101010100=>11010101010110101001 10101010110101010100=>11010101011010101001 10101011010101010100=>11010101101010101001 10101101010101010100=>11010110101010101001 10110101010101010100=>11011010101010101001 11010101010101010100=>11101010101010101001 11111111100000000010=>00000000111111111101 10111111111000000000=>11000000000111111111 11111111010000000010=>11111111100000000101 10111111110100000000=>11011111111000000001 1111111111000000000010=>0000000001111111111101 1011111111110000000000=>1100000000001111111111
Description
Return the rowmotion of the binary word, regarded as a lattice path.
Consider the binary word of length $n$ as a lattice path with $n$ steps, where a 1 corresponds to an up step and a 0 corresponds to a down step.
This map returns the path whose peaks are the valleys of the original path with an up step appended.
Properties
bijective, graded
Sage code
def mapping(w):
    n = len(w)
    w1 = []
    a = 0
    i = 0
    while i < n:
        if w[i]:
            a += 1
            i += 1
        elif i+1 == n:
            w1.extend([1]*(a+1))
            i += 2
            a = 0
        elif w[i+1]:
            w1.extend([1]*(a+1) + [0])
            i += 2
            a = 0
        else:
            w1.append(0)
            i += 1
    w1.extend([0]*a)
    return Word(w1)
Weight
40
Created
Jan 16, 2023 at 17:43 by Martin Rubey
Updated
Jan 16, 2023 at 17:43 by Martin Rubey