# furnasI: Calculation of the Furnas rank for rooted binary trees In treebalance: Computation of Tree (Im)Balance Indices

## Description

This function calculates the Furnas rank F(T) for a given rooted binary tree T. F(T) is the unique rank of the tree T among all rooted binary trees with n leaves in the left-light rooted ordering. For details on the left-light rooted ordering as well as details on how the Furnas rank is computed, see "The generation of random, binary unordered trees" by G.W. Furnas (1984) or "Tree balance indices: a comprehensive survey" by Fischer et al. (2021). The Furnas rank is a balance index.

The concept of assigning each rooted binary tree a unique tuple (rank, n) allows to store many trees with minimal storage use. When the tree gets too big, the function returns Inf.

## Usage

 `1` ```furnasI(tree) ```

## Arguments

 `tree` A rooted binary tree in phylo format.

## Value

`furnasI` returns the unique Furnas rank of the given tree, i.e. the rank of the tree among all rooted binary trees with n leaves in the left-light rooted ordering.

## Author(s)

Luise Kuehn, Lina Herbst

## References

G. W. Furnas. The generation of random, binary unordered trees. Journal of Classification, 1984. doi: 10.1007/bf01890123. URL https://doi.org/10.1007/bf01890123.

M. Kirkpatrick and M. Slatkin. Searching for evolutionary patterns in the shape of a phylogenetic tree. Evolution, 1993. doi: 10.1111/j.1558-5646.1993.tb02144.x.

## Examples

 ```1 2``` ```tree <- ape::read.tree(text="((((,),),(,)),(((,),),(,)));") furnasI(tree) ```

treebalance documentation built on Oct. 17, 2021, 5:06 p.m.