Identifier
Values
[1,0] => [1,0] => 10 => 11 => 0
[1,0,1,0] => [1,0,1,0] => 1010 => 1101 => 2
[1,1,0,0] => [1,1,0,0] => 1100 => 0111 => 1
[1,0,1,0,1,0] => [1,0,1,0,1,0] => 101010 => 110101 => 4
[1,0,1,1,0,0] => [1,0,1,1,0,0] => 101100 => 110011 => 2
[1,1,0,0,1,0] => [1,1,0,0,1,0] => 110010 => 011101 => 3
[1,1,0,1,0,0] => [1,0,1,1,0,0] => 101100 => 110011 => 2
[1,1,1,0,0,0] => [1,1,1,0,0,0] => 111000 => 001111 => 1
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 10101010 => 11010101 => 6
[1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0] => 10101100 => 11010011 => 4
[1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 10110010 => 11001101 => 4
[1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0] => 10101100 => 11010011 => 4
[1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0] => 10111000 => 11000111 => 2
[1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => 11001010 => 01110101 => 5
[1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 11001100 => 01110011 => 3
[1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 10110010 => 11001101 => 4
[1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0] => 11001100 => 01110011 => 3
[1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0] => 10111000 => 11000111 => 2
[1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0] => 11100010 => 00111101 => 3
[1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0] => 11001100 => 01110011 => 3
[1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0] => 10111000 => 11000111 => 2
[1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => 11110000 => 00011111 => 1
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 0001111101 => 3
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0000111111 => 1
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Description
The number of changes of a binary word.
This is the number of indices $i$ such that $w_i \neq w_{i+1}$.
Map
path rowmotion
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.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
bounce path
Description
Sends a Dyck path $D$ of length $2n$ to its bounce path.
This path is formed by starting at the endpoint $(n,n)$ of $D$ and travelling west until encountering the first vertical step of $D$, then south until hitting the diagonal, then west again to hit $D$, etc. until the point $(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.