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
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.
Map
twist
Description
Return the binary word with first letter inverted.