Identifier
Values
[1] => [1,0] => 10 => 00 => 0
[1,1] => [1,0,1,0] => 1010 => 0010 => 0
[2] => [1,1,0,0] => 1100 => 0100 => 0
[1,1,1] => [1,0,1,0,1,0] => 101010 => 001010 => 0
[1,2] => [1,0,1,1,0,0] => 101100 => 001100 => 0
[2,1] => [1,1,0,0,1,0] => 110010 => 010010 => 0
[3] => [1,1,1,0,0,0] => 111000 => 011000 => 1
[1,1,1,1] => [1,0,1,0,1,0,1,0] => 10101010 => 00101010 => 2
[1,1,2] => [1,0,1,0,1,1,0,0] => 10101100 => 00101100 => 0
[1,2,1] => [1,0,1,1,0,0,1,0] => 10110010 => 00110010 => 0
[1,3] => [1,0,1,1,1,0,0,0] => 10111000 => 00111000 => 2
[2,1,1] => [1,1,0,0,1,0,1,0] => 11001010 => 01001010 => 0
[2,2] => [1,1,0,0,1,1,0,0] => 11001100 => 01001100 => 0
[3,1] => [1,1,1,0,0,0,1,0] => 11100010 => 01100010 => 1
[4] => [1,1,1,1,0,0,0,0] => 11110000 => 01110000 => 2
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Description
The number of distinct cubes in a binary word.
A factor of a word is a sequence of consecutive letters. This statistic records the number of distinct non-empty words $u$ such that $uuu$ is a factor of the word.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
twist
Description
Return the binary word with first letter inverted.