Identifier
Values
[1] => [1,0,1,0] => [1,1,0,0] => 1100 => 2
[2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 101100 => 2
[1,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 110100 => 3
[3] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 10101100 => 2
[2,1] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 111000 => 3
[1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => 11010100 => 4
[3,1] => [1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 11001100 => 4
[2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0] => 10110100 => 3
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 11100100 => 2
[3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 10111000 => 3
[3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 11011000 => 2
[2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => 11101000 => 4
[3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 11110000 => 4
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Description
Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
inverse Kreweras complement
Description
Return the inverse of the Kreweras complement of a Dyck path, regarded as a noncrossing set partition.
To identify Dyck paths and noncrossing set partitions, this maps uses the following classical bijection. The number of down steps after the $i$-th up step of the Dyck path is the size of the block of the set partition whose maximal element is $i$. If $i$ is not a maximal element of a block, the $(i+1)$-st step is also an up step.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.