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Identifier
Values
{{1}} => [1] => [.,.] => [[],[]] => 2
{{1,2}} => [2,1] => [[.,.],.] => [[[],[]],[]] => 2
{{1},{2}} => [1,2] => [.,[.,.]] => [[],[[],[]]] => 2
{{1,2,3}} => [2,3,1] => [[.,[.,.]],.] => [[[],[[],[]]],[]] => 2
{{1,2},{3}} => [2,1,3] => [[.,.],[.,.]] => [[[],[]],[[],[]]] => 4
{{1,3},{2}} => [3,2,1] => [[[.,.],.],.] => [[[[],[]],[]],[]] => 2
{{1},{2,3}} => [1,3,2] => [.,[[.,.],.]] => [[],[[[],[]],[]]] => 2
{{1},{2},{3}} => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 2
{{1},{2,3,4}} => [1,3,4,2] => [.,[[.,[.,.]],.]] => [[],[[[],[[],[]]],[]]] => 2
{{1},{2,3},{4}} => [1,3,2,4] => [.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => 4
{{1},{2,4},{3}} => [1,4,3,2] => [.,[[[.,.],.],.]] => [[],[[[[],[]],[]],[]]] => 2
{{1},{2},{3,4}} => [1,2,4,3] => [.,[.,[[.,.],.]]] => [[],[[],[[[],[]],[]]]] => 2
{{1},{2},{3},{4}} => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 2
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Description
The breadth of the ordered tree.
This is the maximal number of nodes having the same depth.
Map
to complete tree
Description
Return the same tree seen as an ordered tree. By default, leaves are transformed into actual nodes.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length 0 to the empty tree, and sending a permutation σ of length n≥1 to a root node with two subtrees L and R by splitting σ at the index σ−1(1), normalizing both sides again to permutations and sending the permutations on the left and on the right of σ−1(1) to the trees L and R, respectively.