Identifier
Values
[1] => [1,0] => 10 => 01 => 0
[2] => [1,0,1,0] => 1010 => 0101 => 0
[1,1] => [1,1,0,0] => 1100 => 1001 => 0
[3] => [1,0,1,0,1,0] => 101010 => 010101 => 1
[2,1] => [1,0,1,1,0,0] => 101100 => 011001 => 0
[1,1,1] => [1,1,0,1,0,0] => 110100 => 101001 => 0
[4] => [1,0,1,0,1,0,1,0] => 10101010 => 01010101 => 2
[3,1] => [1,0,1,0,1,1,0,0] => 10101100 => 01011001 => 0
[2,2] => [1,1,1,0,0,0] => 111000 => 110001 => 1
[2,1,1] => [1,0,1,1,0,1,0,0] => 10110100 => 01101001 => 0
[1,1,1,1] => [1,1,0,1,0,1,0,0] => 11010100 => 10101001 => 1
[3,2] => [1,0,1,1,1,0,0,0] => 10111000 => 01110001 => 2
[2,2,1] => [1,1,1,0,0,1,0,0] => 11100100 => 11001001 => 0
[3,3] => [1,1,1,0,1,0,0,0] => 11101000 => 11010001 => 1
[2,2,2] => [1,1,1,1,0,0,0,0] => 11110000 => 11100001 => 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
rotate front-to-back
Description
The rotation of a binary word, first letter last.
This is the word obtained by moving the first letter to the end.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
to binary word
Description
Return the Dyck word as binary word.