There are

(and possibly some waiting for verification)

**38 statistics**on**Binary trees**in the database:(and possibly some waiting for verification)

St000045Binary trees ⟶ ℤ

The number of linear extensions of a binary tree.

St000050Binary trees ⟶ ℤ

The depth or height of a binary tree.

St000051Binary trees ⟶ ℤ

The size of the left subtree of a binary tree.

St000061Binary trees ⟶ ℤ

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

St000082Binary trees ⟶ ℤ

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

St000083Binary trees ⟶ ℤ

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

St000118Binary trees ⟶ ℤ

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

St000121Binary trees ⟶ ℤ

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

St000122Binary trees ⟶ ℤ

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

St000125Binary trees ⟶ ℤ

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

St000126Binary trees ⟶ ℤ

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

St000127Binary trees ⟶ ℤ

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

St000128Binary trees ⟶ ℤ

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

St000129Binary trees ⟶ ℤ

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

St000130Binary trees ⟶ ℤ

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

St000131Binary trees ⟶ ℤ

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

St000132Binary trees ⟶ ℤ

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

St000161Binary trees ⟶ ℤ

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

St000196Binary trees ⟶ ℤ

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

St000198Binary trees ⟶ ℤ

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

St000201Binary trees ⟶ ℤ

The number of leaf nodes in a binary tree.

St000203Binary trees ⟶ ℤ

The number of external nodes of a binary tree.

St000204Binary trees ⟶ ℤ

The number of internal nodes of a binary tree.

St000252Binary trees ⟶ ℤ

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

St000385Binary trees ⟶ ℤ

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

St000396Binary trees ⟶ ℤ

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

St000398Binary trees ⟶ ℤ

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

St000399Binary trees ⟶ ℤ

The external path length of a binary tree.

St000409Binary trees ⟶ ℤ

The number of pitchforks in a binary tree.

St000411Binary trees ⟶ ℤ

The tree factorial of a binary tree.

St000412Binary trees ⟶ ℤ

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

St000414Binary trees ⟶ ℤ

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

St000568Binary trees ⟶ ℤ

The hook number of a binary tree.

St000569Binary trees ⟶ ℤ

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

St000701Binary trees ⟶ ℤ

The protection number of a binary tree.

St000919Binary trees ⟶ ℤ

The number of maximal left branches of a binary tree.

St001376Binary trees ⟶ ℤ

The Colless index of a binary tree.

St001554Binary trees ⟶ ℤ

The number of distinct nonempty subtrees of a binary tree.