Processing math: 100%

Identifier
Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Images
[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]
>>> Load all 197 entries. <<<
[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]
[] => => [1] => [1]
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.