Identifier
Values
[1] => [1,0] => 10 => 0
[2] => [1,0,1,0] => 1010 => 2
[1,1] => [1,1,0,0] => 1100 => 0
[3] => [1,0,1,0,1,0] => 101010 => 4
[2,1] => [1,0,1,1,0,0] => 101100 => 0
[1,1,1] => [1,1,0,1,0,0] => 110100 => 0
[4] => [1,0,1,0,1,0,1,0] => 10101010 => 6
[3,1] => [1,0,1,0,1,1,0,0] => 10101100 => 0
[2,2] => [1,1,1,0,0,0] => 111000 => 0
[2,1,1] => [1,0,1,1,0,1,0,0] => 10110100 => 0
[1,1,1,1] => [1,1,0,1,0,1,0,0] => 11010100 => 0
[3,2] => [1,0,1,1,1,0,0,0] => 10111000 => 0
[2,2,1] => [1,1,1,0,0,1,0,0] => 11100100 => 0
[3,3] => [1,1,1,0,1,0,0,0] => 11101000 => 0
[2,2,2] => [1,1,1,1,0,0,0,0] => 11110000 => 0
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Description
The length of the border of a binary word.
The border of a word is the longest word which is both a proper prefix and a proper suffix, including a possible empty border.
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.