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

## Contents

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

## Definition

Let a, b be positive integers such that 2 ≤ *a* ≤ (*b*+1)/2. Then a rooted tree T is an (a,b)-tree when:

## Inner node representation

Every inner node v has the following representation:

## References

(a,b)-tree Wikipedia(Text) CC BY-SA