Identifier
Values
[1] => [1,0] => 10 => 00 => 3
[2] => [1,0,1,0] => 1010 => 0010 => 3
[1,1] => [1,1,0,0] => 1100 => 0100 => 2
[3] => [1,0,1,0,1,0] => 101010 => 001010 => 3
[2,1] => [1,0,1,1,0,0] => 101100 => 001100 => 3
[1,1,1] => [1,1,0,1,0,0] => 110100 => 010100 => 2
[4] => [1,0,1,0,1,0,1,0] => 10101010 => 00101010 => 3
[3,1] => [1,0,1,0,1,1,0,0] => 10101100 => 00101100 => 3
[2,2] => [1,1,1,0,0,0] => 111000 => 011000 => 2
[2,1,1] => [1,0,1,1,0,1,0,0] => 10110100 => 00110100 => 3
[1,1,1,1] => [1,1,0,1,0,1,0,0] => 11010100 => 01010100 => 2
[5] => [1,0,1,0,1,0,1,0,1,0] => 1010101010 => 0010101010 => 3
[4,1] => [1,0,1,0,1,0,1,1,0,0] => 1010101100 => 0010101100 => 3
[3,2] => [1,0,1,1,1,0,0,0] => 10111000 => 00111000 => 3
[2,2,1] => [1,1,1,0,0,1,0,0] => 11100100 => 01100100 => 2
[3,3] => [1,1,1,0,1,0,0,0] => 11101000 => 01101000 => 2
[2,2,2] => [1,1,1,1,0,0,0,0] => 11110000 => 01110000 => 2
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Description
The position of the first one in a binary word after appending a 1 at the end.
Regarding the binary word as a subset of $\{1,\dots,n,n+1\}$ that contains $n+1$, this is the minimal element of the set.
Map
to binary word
Description
Return the Dyck word as binary word.
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
twist
Description
Return the binary word with first letter inverted.