The size of a binary tree is its number of internal nodes.

Binary trees of size 1: (the root is on the top and the leafs are not represented)

The number of linear extensions of a binary tree.

The depth/height of a binary tree.

The size of the left subtree of a binary tree.

The number of nodes on the left branch of a binary tree.

The number of elements smaller than a binary tree in Tamari order.

The number of left oriented leafs of a binary tree except the first one.

The number of occurrences of the contiguous pattern [.,[.,[.,.]]] in a binary ....

The number of occurrences of the contiguous pattern [.,[.,[.,[.,.]]]] in a bin....

The number of occurrences of the contiguous pattern [.,[.,[[.,.],.]]] in a bin....

The number of occurrences of the contiguous pattern [.,[[[.,.],.],.

The number of occurrences of the contiguous pattern [.,[.,[.,[.,[.,.]]]]] in a....

The number of occurrences of the contiguous pattern [.,[.,[.,[[.,.],.]]]] in a....

The number of occurrences of the contiguous pattern [.,[.,[[.,[.,.]],.]]] in a....

The number of occurrences of the contiguous pattern [.,[.,[[[.,.],.],.]]] in a....

The number of occurrences of the contiguous pattern [.,[[.,.],[[.,.],.]]] in a....

The number of occurrences of the contiguous pattern [.,[[[[.,.],.],.],.

The number of occurrences of the contiguous pattern [[.,.],[.,[[.,.],.]]] in a....

The sum of the sizes of the right subtrees of a binary tree.

The number of occurrences of the contiguous pattern [[.,.],[.,.

A decimal representation of a binary tree as a code word.

The number of leaf nodes in a binary tree.

The number of external nodes of a binary tree.

The number of internal nodes of a binary tree.

The number of nodes of degree 3 of a binary tree.

The number of vertices with out-degree 1 in a binary tree.

The register function (or Horton-Strahler number) of a binary tree.

The sum of the depths of the vertices (or total internal path length) of a binary....

The external path length of a binary tree.

The number of pitchforks in a binary tree.

The tree factorial of a binary tree.

The number of binary trees with the same underlying unordered tree.

The binary logarithm of the number of binary trees with the same underlying unord....

The hook number of a binary tree.

The sum of the heights of the vertices of a binary tree.

The protection number of a binary tree.

The number of maximal left branches of a binary tree.

Mp00008
Binary trees ⟶ Ordered trees

to complete tree

Mp00009
Binary trees ⟶ Binary trees

left rotate

Mp00010
Binary trees ⟶ Ordered trees

to ordered tree: left child = left brother

to Dyck path: up step, left tree, down step, right tree

Mp00014
Binary trees ⟶ Permutations

to 132-avoiding permutation

Mp00015
Binary trees ⟶ Ordered trees

to ordered tree: right child = right brother

Mp00016
Binary trees ⟶ Binary trees

left-right symmetry

Mp00017
Binary trees ⟶ Permutations

to 312-avoiding permutation

Mp00018
Binary trees ⟶ Binary trees

left border symmetry

Mp00019
Binary trees ⟶ Binary trees

right rotate

to Tamari-corresponding Dyck path

to Tamari-corresponding binary tree

to binary tree: up step, left tree, down step, right tree

Mp00049
Ordered trees ⟶ Binary trees

to binary tree: left brother = left child

Mp00050
Ordered trees ⟶ Binary trees

to binary tree: right brother = right child

Mp00061
Permutations ⟶ Binary trees

to increasing tree

Mp00072
Permutations ⟶ Binary trees

binary search tree: left to right

Mp00139
Ordered trees ⟶ Binary trees

Zeilberger's Strahler bijection

logarithmic height to pruning number

pruning number to logarithmic height