Identifier
Values
[1,0] => 10 => 11 => 11 => 1
[1,0,1,0] => 1010 => 1101 => 1110 => 1
[1,1,0,0] => 1100 => 1101 => 1110 => 1
[1,0,1,0,1,0] => 101010 => 110101 => 111010 => 2
[1,0,1,1,0,0] => 101100 => 110101 => 111010 => 2
[1,1,0,0,1,0] => 110010 => 110101 => 111010 => 2
[1,1,0,1,0,0] => 110100 => 111001 => 111100 => 1
[1,1,1,0,0,0] => 111000 => 111001 => 111100 => 1
[1,0,1,0,1,0,1,0] => 10101010 => 11010101 => 11101010 => 3
[1,0,1,0,1,1,0,0] => 10101100 => 11010101 => 11101010 => 3
[1,0,1,1,0,0,1,0] => 10110010 => 11010101 => 11101010 => 3
[1,0,1,1,0,1,0,0] => 10110100 => 11011001 => 11101100 => 2
[1,0,1,1,1,0,0,0] => 10111000 => 11011001 => 11101100 => 2
[1,1,0,0,1,0,1,0] => 11001010 => 11010101 => 11101010 => 3
[1,1,0,0,1,1,0,0] => 11001100 => 11010101 => 11101010 => 3
[1,1,0,1,0,0,1,0] => 11010010 => 11100101 => 11110010 => 2
[1,1,0,1,0,1,0,0] => 11010100 => 11101001 => 11110100 => 2
[1,1,0,1,1,0,0,0] => 11011000 => 11101001 => 11110100 => 2
[1,1,1,0,0,0,1,0] => 11100010 => 11100101 => 11110010 => 2
[1,1,1,0,0,1,0,0] => 11100100 => 11101001 => 11110100 => 2
[1,1,1,0,1,0,0,0] => 11101000 => 11110001 => 11111000 => 1
[1,1,1,1,0,0,0,0] => 11110000 => 11110001 => 11111000 => 1
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Description
The number of runs of ones in a binary word.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
valleys-to-peaks
Description
Return the binary word with every valley replaced by a peak.
A valley in a binary word is a subsequence $01$, or a trailing $0$. A peak is a subsequence $10$ or a trailing $1$. This map replaces every valley with a peak.
Map
rotate back-to-front
Description
The rotation of a binary word, last letter first.
This is the word obtained by moving the last letter to the beginnig.