furnasI | R Documentation |

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. (2023). 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.

For details on the Furnas rank, see
also Chapter 22 in "Tree balance indices: a comprehensive survey" (https://doi.org/10.1007/978-3-031-39800-1_22).

```
furnasI(tree)
```

`tree` |
A rooted binary tree in phylo format. |

`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. Since the values can get quite large, the function
returns them in `big.z`

format (package `gmp`

).

Luise Kuehn, Lina Herbst

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.

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

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