Processing math: 100%

Identifier
Values
[1,0] => [1,0] => 10 => 00 => 0
[1,0,1,0] => [1,1,0,0] => 1100 => 0100 => 1
[1,1,0,0] => [1,0,1,0] => 1010 => 0010 => 1
[1,0,1,0,1,0] => [1,1,1,0,0,0] => 111000 => 011000 => 1
[1,0,1,1,0,0] => [1,0,1,1,0,0] => 101100 => 001100 => 1
[1,1,0,0,1,0] => [1,1,0,1,0,0] => 110100 => 010100 => 2
[1,1,0,1,0,0] => [1,1,0,0,1,0] => 110010 => 010010 => 2
[1,1,1,0,0,0] => [1,0,1,0,1,0] => 101010 => 001010 => 2
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 11110000 => 01110000 => 1
[1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 10111000 => 00111000 => 1
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 11011000 => 01011000 => 2
[1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0] => 11100010 => 01100010 => 2
[1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 10101100 => 00101100 => 2
[1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 11101000 => 01101000 => 2
[1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0] => 10110100 => 00110100 => 2
[1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 11100100 => 01100100 => 2
[1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0] => 11001100 => 01001100 => 2
[1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0] => 10110010 => 00110010 => 2
[1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0] => 11010100 => 01010100 => 3
[1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 11010010 => 01010010 => 3
[1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0] => 11001010 => 01001010 => 3
[1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 10101010 => 00101010 => 3
[1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 1010101100 => 0010101100 => 3
[1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1010101010 => 0010101010 => 4
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Description
The number of runs of ones in a binary word.
Map
inverse zeta map
Description
The inverse zeta map on Dyck paths.
See its inverse, the zeta map Mp00030zeta map, for the definition and details.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
twist
Description
Return the binary word with first letter inverted.