Identifier
Mp00034:
Dyck paths
—to binary tree: up step, left tree, down step, right tree⟶
Binary trees
Mp00010: Binary trees —to ordered tree: left child = left brother⟶ Ordered trees
Mp00010: Binary trees —to ordered tree: left child = left brother⟶ Ordered trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-1Cc0021;cc-rep-2
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[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[],[[]],[],[],[],[[]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[[],[[]],[],[],[[]],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[[],[[]],[],[[]],[],[]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[[],[[]],[[]],[],[],[]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[[],[[[]]],[],[],[],[]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[[],[[],[]],[],[],[],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[[]],[],[],[],[],[[]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[[[]],[],[],[],[[]],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[[[]],[],[],[[]],[],[]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[[[]],[],[[]],[],[],[]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[]],[[]],[],[],[],[]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[[[[]]],[],[],[],[],[]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[[[],[]],[],[],[],[],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[],[],[],[],[],[],[[]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[[],[],[],[],[[]],[],[]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[[],[],[],[[]],[],[],[]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[[],[],[[]],[],[],[],[]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[[],[[]],[],[],[],[],[]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[[[]],[],[],[],[],[],[]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[[],[],[],[],[],[],[],[]]
Map
to binary tree: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
Map
to ordered tree: left child = left brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
- if $x$ is the left child of $y$, $x$ becomes the left brother of $y$,
- if $x$ is the right child of $y$, $x$ becomes the last child of $y$.
searching the database
Sorry, this map was not found in the database.