Identifier
Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Images
=>
Cc0005;cc-rep-0
[1,0]=>10=>[1,2]=>[1,2] [1,0,1,0]=>1010=>[1,2,2]=>[1,2,2] [1,1,0,0]=>1100=>[1,1,3]=>[1,1,3] [1,0,1,0,1,0]=>101010=>[1,2,2,2]=>[1,2,2,2] [1,0,1,1,0,0]=>101100=>[1,2,1,3]=>[1,1,3,2] [1,1,0,0,1,0]=>110010=>[1,1,3,2]=>[1,2,1,3] [1,1,0,1,0,0]=>110100=>[1,1,2,3]=>[1,1,2,3] [1,1,1,0,0,0]=>111000=>[1,1,1,4]=>[1,1,1,4] [1,0,1,0,1,0,1,0]=>10101010=>[1,2,2,2,2]=>[1,2,2,2,2] [1,0,1,0,1,1,0,0]=>10101100=>[1,2,2,1,3]=>[1,1,3,2,2] [1,0,1,1,0,0,1,0]=>10110010=>[1,2,1,3,2]=>[1,2,1,3,2] [1,0,1,1,0,1,0,0]=>10110100=>[1,2,1,2,3]=>[1,1,2,3,2] [1,0,1,1,1,0,0,0]=>10111000=>[1,2,1,1,4]=>[1,1,1,4,2] [1,1,0,0,1,0,1,0]=>11001010=>[1,1,3,2,2]=>[1,2,2,1,3] [1,1,0,0,1,1,0,0]=>11001100=>[1,1,3,1,3]=>[1,1,3,1,3] [1,1,0,1,0,0,1,0]=>11010010=>[1,1,2,3,2]=>[1,2,1,2,3] [1,1,0,1,0,1,0,0]=>11010100=>[1,1,2,2,3]=>[1,1,2,2,3] [1,1,0,1,1,0,0,0]=>11011000=>[1,1,2,1,4]=>[1,1,1,3,3] [1,1,1,0,0,0,1,0]=>11100010=>[1,1,1,4,2]=>[1,2,1,1,4] [1,1,1,0,0,1,0,0]=>11100100=>[1,1,1,3,3]=>[1,1,2,1,4] [1,1,1,0,1,0,0,0]=>11101000=>[1,1,1,2,4]=>[1,1,1,2,4] [1,1,1,1,0,0,0,0]=>11110000=>[1,1,1,1,5]=>[1,1,1,1,5] [1,0,1,0,1,0,1,0,1,0]=>1010101010=>[1,2,2,2,2,2]=>[1,2,2,2,2,2] [1,0,1,0,1,0,1,1,0,0]=>1010101100=>[1,2,2,2,1,3]=>[1,1,3,2,2,2] [1,0,1,0,1,1,0,0,1,0]=>1010110010=>[1,2,2,1,3,2]=>[1,2,1,3,2,2] [1,0,1,0,1,1,0,1,0,0]=>1010110100=>[1,2,2,1,2,3]=>[1,1,2,3,2,2] [1,0,1,0,1,1,1,0,0,0]=>1010111000=>[1,2,2,1,1,4]=>[1,1,1,4,2,2] [1,0,1,1,0,0,1,0,1,0]=>1011001010=>[1,2,1,3,2,2]=>[1,2,2,1,3,2] [1,0,1,1,0,0,1,1,0,0]=>1011001100=>[1,2,1,3,1,3]=>[1,1,3,1,3,2] [1,0,1,1,0,1,0,0,1,0]=>1011010010=>[1,2,1,2,3,2]=>[1,2,1,2,3,2] [1,0,1,1,0,1,0,1,0,0]=>1011010100=>[1,2,1,2,2,3]=>[1,1,2,2,3,2] [1,0,1,1,0,1,1,0,0,0]=>1011011000=>[1,2,1,2,1,4]=>[1,1,1,3,3,2] [1,0,1,1,1,0,0,0,1,0]=>1011100010=>[1,2,1,1,4,2]=>[1,2,1,1,4,2] [1,0,1,1,1,0,0,1,0,0]=>1011100100=>[1,2,1,1,3,3]=>[1,1,2,1,4,2] [1,0,1,1,1,0,1,0,0,0]=>1011101000=>[1,2,1,1,2,4]=>[1,1,1,2,4,2] [1,0,1,1,1,1,0,0,0,0]=>1011110000=>[1,2,1,1,1,5]=>[1,1,1,1,5,2] [1,1,0,0,1,0,1,0,1,0]=>1100101010=>[1,1,3,2,2,2]=>[1,2,2,2,1,3] [1,1,0,0,1,0,1,1,0,0]=>1100101100=>[1,1,3,2,1,3]=>[1,1,3,2,1,3] [1,1,0,0,1,1,0,0,1,0]=>1100110010=>[1,1,3,1,3,2]=>[1,2,1,3,1,3] [1,1,0,0,1,1,0,1,0,0]=>1100110100=>[1,1,3,1,2,3]=>[1,1,2,3,1,3] [1,1,0,0,1,1,1,0,0,0]=>1100111000=>[1,1,3,1,1,4]=>[1,1,1,4,1,3] [1,1,0,1,0,0,1,0,1,0]=>1101001010=>[1,1,2,3,2,2]=>[1,2,2,1,2,3] [1,1,0,1,0,0,1,1,0,0]=>1101001100=>[1,1,2,3,1,3]=>[1,1,3,1,2,3] [1,1,0,1,0,1,0,0,1,0]=>1101010010=>[1,1,2,2,3,2]=>[1,2,1,2,2,3] [1,1,0,1,0,1,0,1,0,0]=>1101010100=>[1,1,2,2,2,3]=>[1,1,2,2,2,3] [1,1,0,1,0,1,1,0,0,0]=>1101011000=>[1,1,2,2,1,4]=>[1,1,1,3,2,3] [1,1,0,1,1,0,0,0,1,0]=>1101100010=>[1,1,2,1,4,2]=>[1,2,1,1,3,3] [1,1,0,1,1,0,0,1,0,0]=>1101100100=>[1,1,2,1,3,3]=>[1,1,2,1,3,3] [1,1,0,1,1,0,1,0,0,0]=>1101101000=>[1,1,2,1,2,4]=>[1,1,1,2,3,3] [1,1,0,1,1,1,0,0,0,0]=>1101110000=>[1,1,2,1,1,5]=>[1,1,1,1,4,3] [1,1,1,0,0,0,1,0,1,0]=>1110001010=>[1,1,1,4,2,2]=>[1,2,2,1,1,4] [1,1,1,0,0,0,1,1,0,0]=>1110001100=>[1,1,1,4,1,3]=>[1,1,3,1,1,4] [1,1,1,0,0,1,0,0,1,0]=>1110010010=>[1,1,1,3,3,2]=>[1,2,1,2,1,4] [1,1,1,0,0,1,0,1,0,0]=>1110010100=>[1,1,1,3,2,3]=>[1,1,2,2,1,4] [1,1,1,0,0,1,1,0,0,0]=>1110011000=>[1,1,1,3,1,4]=>[1,1,1,3,1,4] [1,1,1,0,1,0,0,0,1,0]=>1110100010=>[1,1,1,2,4,2]=>[1,2,1,1,2,4] [1,1,1,0,1,0,0,1,0,0]=>1110100100=>[1,1,1,2,3,3]=>[1,1,2,1,2,4] [1,1,1,0,1,0,1,0,0,0]=>1110101000=>[1,1,1,2,2,4]=>[1,1,1,2,2,4] [1,1,1,0,1,1,0,0,0,0]=>1110110000=>[1,1,1,2,1,5]=>[1,1,1,1,3,4] [1,1,1,1,0,0,0,0,1,0]=>1111000010=>[1,1,1,1,5,2]=>[1,2,1,1,1,5] [1,1,1,1,0,0,0,1,0,0]=>1111000100=>[1,1,1,1,4,3]=>[1,1,2,1,1,5] [1,1,1,1,0,0,1,0,0,0]=>1111001000=>[1,1,1,1,3,4]=>[1,1,1,2,1,5] [1,1,1,1,0,1,0,0,0,0]=>1111010000=>[1,1,1,1,2,5]=>[1,1,1,1,2,5] [1,1,1,1,1,0,0,0,0,0]=>1111100000=>[1,1,1,1,1,6]=>[1,1,1,1,1,6] [1,0,1,0,1,0,1,0,1,0,1,0]=>101010101010=>[1,2,2,2,2,2,2]=>[1,2,2,2,2,2,2] [1,0,1,0,1,0,1,0,1,1,0,0]=>101010101100=>[1,2,2,2,2,1,3]=>[1,1,3,2,2,2,2] [1,0,1,0,1,0,1,1,0,0,1,0]=>101010110010=>[1,2,2,2,1,3,2]=>[1,2,1,3,2,2,2] [1,0,1,0,1,0,1,1,0,1,0,0]=>101010110100=>[1,2,2,2,1,2,3]=>[1,1,2,3,2,2,2] [1,0,1,0,1,0,1,1,1,0,0,0]=>101010111000=>[1,2,2,2,1,1,4]=>[1,1,1,4,2,2,2] [1,0,1,0,1,1,0,0,1,0,1,0]=>101011001010=>[1,2,2,1,3,2,2]=>[1,2,2,1,3,2,2] [1,0,1,0,1,1,0,0,1,1,0,0]=>101011001100=>[1,2,2,1,3,1,3]=>[1,1,3,1,3,2,2] [1,0,1,0,1,1,0,1,0,0,1,0]=>101011010010=>[1,2,2,1,2,3,2]=>[1,2,1,2,3,2,2] [1,0,1,0,1,1,0,1,0,1,0,0]=>101011010100=>[1,2,2,1,2,2,3]=>[1,1,2,2,3,2,2] [1,0,1,0,1,1,0,1,1,0,0,0]=>101011011000=>[1,2,2,1,2,1,4]=>[1,1,1,3,3,2,2] [1,0,1,0,1,1,1,0,0,0,1,0]=>101011100010=>[1,2,2,1,1,4,2]=>[1,2,1,1,4,2,2] [1,0,1,0,1,1,1,0,0,1,0,0]=>101011100100=>[1,2,2,1,1,3,3]=>[1,1,2,1,4,2,2] [1,0,1,0,1,1,1,0,1,0,0,0]=>101011101000=>[1,2,2,1,1,2,4]=>[1,1,1,2,4,2,2] [1,0,1,0,1,1,1,1,0,0,0,0]=>101011110000=>[1,2,2,1,1,1,5]=>[1,1,1,1,5,2,2] [1,0,1,1,0,0,1,0,1,0,1,0]=>101100101010=>[1,2,1,3,2,2,2]=>[1,2,2,2,1,3,2] [1,0,1,1,0,0,1,0,1,1,0,0]=>101100101100=>[1,2,1,3,2,1,3]=>[1,1,3,2,1,3,2] [1,0,1,1,0,0,1,1,0,0,1,0]=>101100110010=>[1,2,1,3,1,3,2]=>[1,2,1,3,1,3,2] [1,0,1,1,0,0,1,1,0,1,0,0]=>101100110100=>[1,2,1,3,1,2,3]=>[1,1,2,3,1,3,2] [1,0,1,1,0,0,1,1,1,0,0,0]=>101100111000=>[1,2,1,3,1,1,4]=>[1,1,1,4,1,3,2] [1,0,1,1,0,1,0,0,1,0,1,0]=>101101001010=>[1,2,1,2,3,2,2]=>[1,2,2,1,2,3,2] [1,0,1,1,0,1,0,0,1,1,0,0]=>101101001100=>[1,2,1,2,3,1,3]=>[1,1,3,1,2,3,2] [1,0,1,1,0,1,0,1,0,0,1,0]=>101101010010=>[1,2,1,2,2,3,2]=>[1,2,1,2,2,3,2] [1,0,1,1,0,1,0,1,0,1,0,0]=>101101010100=>[1,2,1,2,2,2,3]=>[1,1,2,2,2,3,2] [1,0,1,1,0,1,0,1,1,0,0,0]=>101101011000=>[1,2,1,2,2,1,4]=>[1,1,1,3,2,3,2] [1,0,1,1,0,1,1,0,0,0,1,0]=>101101100010=>[1,2,1,2,1,4,2]=>[1,2,1,1,3,3,2] [1,0,1,1,0,1,1,0,0,1,0,0]=>101101100100=>[1,2,1,2,1,3,3]=>[1,1,2,1,3,3,2] [1,0,1,1,0,1,1,0,1,0,0,0]=>101101101000=>[1,2,1,2,1,2,4]=>[1,1,1,2,3,3,2] [1,0,1,1,0,1,1,1,0,0,0,0]=>101101110000=>[1,2,1,2,1,1,5]=>[1,1,1,1,4,3,2] [1,0,1,1,1,0,0,0,1,0,1,0]=>101110001010=>[1,2,1,1,4,2,2]=>[1,2,2,1,1,4,2] [1,0,1,1,1,0,0,0,1,1,0,0]=>101110001100=>[1,2,1,1,4,1,3]=>[1,1,3,1,1,4,2] [1,0,1,1,1,0,0,1,0,0,1,0]=>101110010010=>[1,2,1,1,3,3,2]=>[1,2,1,2,1,4,2] [1,0,1,1,1,0,0,1,0,1,0,0]=>101110010100=>[1,2,1,1,3,2,3]=>[1,1,2,2,1,4,2] [1,0,1,1,1,0,0,1,1,0,0,0]=>101110011000=>[1,2,1,1,3,1,4]=>[1,1,1,3,1,4,2] [1,0,1,1,1,0,1,0,0,0,1,0]=>101110100010=>[1,2,1,1,2,4,2]=>[1,2,1,1,2,4,2] [1,0,1,1,1,0,1,0,0,1,0,0]=>101110100100=>[1,2,1,1,2,3,3]=>[1,1,2,1,2,4,2] [1,0,1,1,1,0,1,0,1,0,0,0]=>101110101000=>[1,2,1,1,2,2,4]=>[1,1,1,2,2,4,2] [1,0,1,1,1,0,1,1,0,0,0,0]=>101110110000=>[1,2,1,1,2,1,5]=>[1,1,1,1,3,4,2] [1,0,1,1,1,1,0,0,0,0,1,0]=>101111000010=>[1,2,1,1,1,5,2]=>[1,2,1,1,1,5,2] [1,0,1,1,1,1,0,0,0,1,0,0]=>101111000100=>[1,2,1,1,1,4,3]=>[1,1,2,1,1,5,2] [1,0,1,1,1,1,0,0,1,0,0,0]=>101111001000=>[1,2,1,1,1,3,4]=>[1,1,1,2,1,5,2] [1,0,1,1,1,1,0,1,0,0,0,0]=>101111010000=>[1,2,1,1,1,2,5]=>[1,1,1,1,2,5,2] [1,0,1,1,1,1,1,0,0,0,0,0]=>101111100000=>[1,2,1,1,1,1,6]=>[1,1,1,1,1,6,2] [1,1,0,0,1,0,1,0,1,0,1,0]=>110010101010=>[1,1,3,2,2,2,2]=>[1,2,2,2,2,1,3] [1,1,0,0,1,0,1,0,1,1,0,0]=>110010101100=>[1,1,3,2,2,1,3]=>[1,1,3,2,2,1,3] [1,1,0,0,1,0,1,1,0,0,1,0]=>110010110010=>[1,1,3,2,1,3,2]=>[1,2,1,3,2,1,3] [1,1,0,0,1,0,1,1,0,1,0,0]=>110010110100=>[1,1,3,2,1,2,3]=>[1,1,2,3,2,1,3] [1,1,0,0,1,0,1,1,1,0,0,0]=>110010111000=>[1,1,3,2,1,1,4]=>[1,1,1,4,2,1,3] [1,1,0,0,1,1,0,0,1,0,1,0]=>110011001010=>[1,1,3,1,3,2,2]=>[1,2,2,1,3,1,3] [1,1,0,0,1,1,0,0,1,1,0,0]=>110011001100=>[1,1,3,1,3,1,3]=>[1,1,3,1,3,1,3] [1,1,0,0,1,1,0,1,0,0,1,0]=>110011010010=>[1,1,3,1,2,3,2]=>[1,2,1,2,3,1,3] [1,1,0,0,1,1,0,1,0,1,0,0]=>110011010100=>[1,1,3,1,2,2,3]=>[1,1,2,2,3,1,3] [1,1,0,0,1,1,0,1,1,0,0,0]=>110011011000=>[1,1,3,1,2,1,4]=>[1,1,1,3,3,1,3] [1,1,0,0,1,1,1,0,0,0,1,0]=>110011100010=>[1,1,3,1,1,4,2]=>[1,2,1,1,4,1,3] [1,1,0,0,1,1,1,0,0,1,0,0]=>110011100100=>[1,1,3,1,1,3,3]=>[1,1,2,1,4,1,3] [1,1,0,0,1,1,1,0,1,0,0,0]=>110011101000=>[1,1,3,1,1,2,4]=>[1,1,1,2,4,1,3] [1,1,0,0,1,1,1,1,0,0,0,0]=>110011110000=>[1,1,3,1,1,1,5]=>[1,1,1,1,5,1,3] [1,1,0,1,0,0,1,0,1,0,1,0]=>110100101010=>[1,1,2,3,2,2,2]=>[1,2,2,2,1,2,3] [1,1,0,1,0,0,1,0,1,1,0,0]=>110100101100=>[1,1,2,3,2,1,3]=>[1,1,3,2,1,2,3] [1,1,0,1,0,0,1,1,0,0,1,0]=>110100110010=>[1,1,2,3,1,3,2]=>[1,2,1,3,1,2,3] [1,1,0,1,0,0,1,1,0,1,0,0]=>110100110100=>[1,1,2,3,1,2,3]=>[1,1,2,3,1,2,3] [1,1,0,1,0,0,1,1,1,0,0,0]=>110100111000=>[1,1,2,3,1,1,4]=>[1,1,1,4,1,2,3] [1,1,0,1,0,1,0,0,1,0,1,0]=>110101001010=>[1,1,2,2,3,2,2]=>[1,2,2,1,2,2,3] [1,1,0,1,0,1,0,0,1,1,0,0]=>110101001100=>[1,1,2,2,3,1,3]=>[1,1,3,1,2,2,3] [1,1,0,1,0,1,0,1,0,0,1,0]=>110101010010=>[1,1,2,2,2,3,2]=>[1,2,1,2,2,2,3] [1,1,0,1,0,1,0,1,0,1,0,0]=>110101010100=>[1,1,2,2,2,2,3]=>[1,1,2,2,2,2,3] [1,1,0,1,0,1,0,1,1,0,0,0]=>110101011000=>[1,1,2,2,2,1,4]=>[1,1,1,3,2,2,3] [1,1,0,1,0,1,1,0,0,0,1,0]=>110101100010=>[1,1,2,2,1,4,2]=>[1,2,1,1,3,2,3] [1,1,0,1,0,1,1,0,0,1,0,0]=>110101100100=>[1,1,2,2,1,3,3]=>[1,1,2,1,3,2,3] [1,1,0,1,0,1,1,0,1,0,0,0]=>110101101000=>[1,1,2,2,1,2,4]=>[1,1,1,2,3,2,3] [1,1,0,1,0,1,1,1,0,0,0,0]=>110101110000=>[1,1,2,2,1,1,5]=>[1,1,1,1,4,2,3] [1,1,0,1,1,0,0,0,1,0,1,0]=>110110001010=>[1,1,2,1,4,2,2]=>[1,2,2,1,1,3,3] [1,1,0,1,1,0,0,0,1,1,0,0]=>110110001100=>[1,1,2,1,4,1,3]=>[1,1,3,1,1,3,3] [1,1,0,1,1,0,0,1,0,0,1,0]=>110110010010=>[1,1,2,1,3,3,2]=>[1,2,1,2,1,3,3] [1,1,0,1,1,0,0,1,0,1,0,0]=>110110010100=>[1,1,2,1,3,2,3]=>[1,1,2,2,1,3,3] [1,1,0,1,1,0,0,1,1,0,0,0]=>110110011000=>[1,1,2,1,3,1,4]=>[1,1,1,3,1,3,3] [1,1,0,1,1,0,1,0,0,0,1,0]=>110110100010=>[1,1,2,1,2,4,2]=>[1,2,1,1,2,3,3] [1,1,0,1,1,0,1,0,0,1,0,0]=>110110100100=>[1,1,2,1,2,3,3]=>[1,1,2,1,2,3,3] [1,1,0,1,1,0,1,0,1,0,0,0]=>110110101000=>[1,1,2,1,2,2,4]=>[1,1,1,2,2,3,3] [1,1,0,1,1,0,1,1,0,0,0,0]=>110110110000=>[1,1,2,1,2,1,5]=>[1,1,1,1,3,3,3] [1,1,0,1,1,1,0,0,0,0,1,0]=>110111000010=>[1,1,2,1,1,5,2]=>[1,2,1,1,1,4,3] [1,1,0,1,1,1,0,0,0,1,0,0]=>110111000100=>[1,1,2,1,1,4,3]=>[1,1,2,1,1,4,3] [1,1,0,1,1,1,0,0,1,0,0,0]=>110111001000=>[1,1,2,1,1,3,4]=>[1,1,1,2,1,4,3] [1,1,0,1,1,1,0,1,0,0,0,0]=>110111010000=>[1,1,2,1,1,2,5]=>[1,1,1,1,2,4,3] [1,1,0,1,1,1,1,0,0,0,0,0]=>110111100000=>[1,1,2,1,1,1,6]=>[1,1,1,1,1,5,3] [1,1,1,0,0,0,1,0,1,0,1,0]=>111000101010=>[1,1,1,4,2,2,2]=>[1,2,2,2,1,1,4] [1,1,1,0,0,0,1,0,1,1,0,0]=>111000101100=>[1,1,1,4,2,1,3]=>[1,1,3,2,1,1,4] [1,1,1,0,0,0,1,1,0,0,1,0]=>111000110010=>[1,1,1,4,1,3,2]=>[1,2,1,3,1,1,4] [1,1,1,0,0,0,1,1,0,1,0,0]=>111000110100=>[1,1,1,4,1,2,3]=>[1,1,2,3,1,1,4] [1,1,1,0,0,0,1,1,1,0,0,0]=>111000111000=>[1,1,1,4,1,1,4]=>[1,1,1,4,1,1,4] [1,1,1,0,0,1,0,0,1,0,1,0]=>111001001010=>[1,1,1,3,3,2,2]=>[1,2,2,1,2,1,4] [1,1,1,0,0,1,0,0,1,1,0,0]=>111001001100=>[1,1,1,3,3,1,3]=>[1,1,3,1,2,1,4] [1,1,1,0,0,1,0,1,0,0,1,0]=>111001010010=>[1,1,1,3,2,3,2]=>[1,2,1,2,2,1,4] [1,1,1,0,0,1,0,1,0,1,0,0]=>111001010100=>[1,1,1,3,2,2,3]=>[1,1,2,2,2,1,4] [1,1,1,0,0,1,0,1,1,0,0,0]=>111001011000=>[1,1,1,3,2,1,4]=>[1,1,1,3,2,1,4] [1,1,1,0,0,1,1,0,0,0,1,0]=>111001100010=>[1,1,1,3,1,4,2]=>[1,2,1,1,3,1,4] [1,1,1,0,0,1,1,0,0,1,0,0]=>111001100100=>[1,1,1,3,1,3,3]=>[1,1,2,1,3,1,4] [1,1,1,0,0,1,1,0,1,0,0,0]=>111001101000=>[1,1,1,3,1,2,4]=>[1,1,1,2,3,1,4] [1,1,1,0,0,1,1,1,0,0,0,0]=>111001110000=>[1,1,1,3,1,1,5]=>[1,1,1,1,4,1,4] [1,1,1,0,1,0,0,0,1,0,1,0]=>111010001010=>[1,1,1,2,4,2,2]=>[1,2,2,1,1,2,4] [1,1,1,0,1,0,0,0,1,1,0,0]=>111010001100=>[1,1,1,2,4,1,3]=>[1,1,3,1,1,2,4] [1,1,1,0,1,0,0,1,0,0,1,0]=>111010010010=>[1,1,1,2,3,3,2]=>[1,2,1,2,1,2,4] [1,1,1,0,1,0,0,1,0,1,0,0]=>111010010100=>[1,1,1,2,3,2,3]=>[1,1,2,2,1,2,4] [1,1,1,0,1,0,0,1,1,0,0,0]=>111010011000=>[1,1,1,2,3,1,4]=>[1,1,1,3,1,2,4] [1,1,1,0,1,0,1,0,0,0,1,0]=>111010100010=>[1,1,1,2,2,4,2]=>[1,2,1,1,2,2,4] [1,1,1,0,1,0,1,0,0,1,0,0]=>111010100100=>[1,1,1,2,2,3,3]=>[1,1,2,1,2,2,4] [1,1,1,0,1,0,1,0,1,0,0,0]=>111010101000=>[1,1,1,2,2,2,4]=>[1,1,1,2,2,2,4] [1,1,1,0,1,0,1,1,0,0,0,0]=>111010110000=>[1,1,1,2,2,1,5]=>[1,1,1,1,3,2,4] [1,1,1,0,1,1,0,0,0,0,1,0]=>111011000010=>[1,1,1,2,1,5,2]=>[1,2,1,1,1,3,4] [1,1,1,0,1,1,0,0,0,1,0,0]=>111011000100=>[1,1,1,2,1,4,3]=>[1,1,2,1,1,3,4] [1,1,1,0,1,1,0,0,1,0,0,0]=>111011001000=>[1,1,1,2,1,3,4]=>[1,1,1,2,1,3,4] [1,1,1,0,1,1,0,1,0,0,0,0]=>111011010000=>[1,1,1,2,1,2,5]=>[1,1,1,1,2,3,4] [1,1,1,0,1,1,1,0,0,0,0,0]=>111011100000=>[1,1,1,2,1,1,6]=>[1,1,1,1,1,4,4] [1,1,1,1,0,0,0,0,1,0,1,0]=>111100001010=>[1,1,1,1,5,2,2]=>[1,2,2,1,1,1,5] [1,1,1,1,0,0,0,0,1,1,0,0]=>111100001100=>[1,1,1,1,5,1,3]=>[1,1,3,1,1,1,5] [1,1,1,1,0,0,0,1,0,0,1,0]=>111100010010=>[1,1,1,1,4,3,2]=>[1,2,1,2,1,1,5] [1,1,1,1,0,0,0,1,0,1,0,0]=>111100010100=>[1,1,1,1,4,2,3]=>[1,1,2,2,1,1,5] [1,1,1,1,0,0,0,1,1,0,0,0]=>111100011000=>[1,1,1,1,4,1,4]=>[1,1,1,3,1,1,5] [1,1,1,1,0,0,1,0,0,0,1,0]=>111100100010=>[1,1,1,1,3,4,2]=>[1,2,1,1,2,1,5] [1,1,1,1,0,0,1,0,0,1,0,0]=>111100100100=>[1,1,1,1,3,3,3]=>[1,1,2,1,2,1,5] [1,1,1,1,0,0,1,0,1,0,0,0]=>111100101000=>[1,1,1,1,3,2,4]=>[1,1,1,2,2,1,5] [1,1,1,1,0,0,1,1,0,0,0,0]=>111100110000=>[1,1,1,1,3,1,5]=>[1,1,1,1,3,1,5] [1,1,1,1,0,1,0,0,0,0,1,0]=>111101000010=>[1,1,1,1,2,5,2]=>[1,2,1,1,1,2,5] [1,1,1,1,0,1,0,0,0,1,0,0]=>111101000100=>[1,1,1,1,2,4,3]=>[1,1,2,1,1,2,5] [1,1,1,1,0,1,0,0,1,0,0,0]=>111101001000=>[1,1,1,1,2,3,4]=>[1,1,1,2,1,2,5] [1,1,1,1,0,1,0,1,0,0,0,0]=>111101010000=>[1,1,1,1,2,2,5]=>[1,1,1,1,2,2,5] [1,1,1,1,0,1,1,0,0,0,0,0]=>111101100000=>[1,1,1,1,2,1,6]=>[1,1,1,1,1,3,5] [1,1,1,1,1,0,0,0,0,0,1,0]=>111110000010=>[1,1,1,1,1,6,2]=>[1,2,1,1,1,1,6] [1,1,1,1,1,0,0,0,0,1,0,0]=>111110000100=>[1,1,1,1,1,5,3]=>[1,1,2,1,1,1,6] [1,1,1,1,1,0,0,0,1,0,0,0]=>111110001000=>[1,1,1,1,1,4,4]=>[1,1,1,2,1,1,6] [1,1,1,1,1,0,0,1,0,0,0,0]=>111110010000=>[1,1,1,1,1,3,5]=>[1,1,1,1,2,1,6] [1,1,1,1,1,0,1,0,0,0,0,0]=>111110100000=>[1,1,1,1,1,2,6]=>[1,1,1,1,1,2,6] [1,1,1,1,1,1,0,0,0,0,0,0]=>111111000000=>[1,1,1,1,1,1,7]=>[1,1,1,1,1,1,7]
Map
to binary word
Description
Return the Dyck word as binary word.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Map
conjugate
Description
The conjugate of a composition.
The conjugate of a composition $C$ is defined as the complement (Mp00039complement) of the reversal (Mp00038reverse) of $C$.
Equivalently, the ribbon shape corresponding to the conjugate of $C$ is the conjugate of the ribbon shape of $C$.