Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-2
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[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.]=>[6,7,5,4,3,2,1,8,9,10,11]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.]=>[6,7,5,4,3,2,1,8,9,10]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.]=>[5,6,4,3,2,7,1,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[[[.,.],.],[[[.,[[[.,.],.],.]],.],.]]=>[1,2,5,6,7,4,8,9,3]=>[.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[6,7,5,4,3,2,1,8,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]=>[5,4,3,2,1,8,9,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[7,6,5,4,3,2,1,9,10,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
searching the database
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