Identifier
Values
[1] => [1,0] => 10 => 01 => 1
[1,1] => [1,0,1,0] => 1010 => 0101 => 2
[2] => [1,1,0,0] => 1100 => 0011 => 1
[1,1,1] => [1,0,1,0,1,0] => 101010 => 010101 => 3
[1,2] => [1,0,1,1,0,0] => 101100 => 010011 => 2
[2,1] => [1,1,0,0,1,0] => 110010 => 001101 => 1
[3] => [1,1,1,0,0,0] => 111000 => 000111 => 1
[1,1,1,1] => [1,0,1,0,1,0,1,0] => 10101010 => 01010101 => 4
[1,1,2] => [1,0,1,0,1,1,0,0] => 10101100 => 01010011 => 3
[1,2,1] => [1,0,1,1,0,0,1,0] => 10110010 => 01001101 => 2
[1,3] => [1,0,1,1,1,0,0,0] => 10111000 => 01000111 => 2
[2,1,1] => [1,1,0,0,1,0,1,0] => 11001010 => 00110101 => 1
[2,2] => [1,1,0,0,1,1,0,0] => 11001100 => 00110011 => 2
[3,1] => [1,1,1,0,0,0,1,0] => 11100010 => 00011101 => 1
[4] => [1,1,1,1,0,0,0,0] => 11110000 => 00001111 => 1
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Description
The length of the Lyndon factorization of the binary word.
The Lyndon factorization of a finite word w is its unique factorization as a non-increasing product of Lyndon words, i.e., $w = l_1\dots l_n$ where each $l_i$ is a Lyndon word and $l_1 \geq\dots\geq l_n$.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.