# (a,b)-tree

In computer science, an (a,b) tree is a specific kind of search tree.

An (a,b) tree has all of its leaves at the same depth, and all internal nodes except for the root have between ${\displaystyle a}$ and ${\displaystyle b}$ children, where ${\displaystyle a}$ and ${\displaystyle b}$ are integers such that ${\displaystyle 2\leq a\leq (b+1)/2}$. The root has, if it is not a leaf, between 2 and b children.

## Definition

Let ${\displaystyle a,b\in \mathbb {N} }$ such that ${\displaystyle a\leq b}$. Then a tree T is an (a,b) tree when:

## Inner node representation

Every inner node ${\displaystyle v}$ has the following representation: