furnasI_inv | R Documentation |

This function calculates the unique tree `T`

(in phylo format) for two
given integer values `r`

and `n`

, with `n`

denoting the number
of leaves of `T`

and `r`

denoting the rank of `T`

in the
left-light rooted ordering of all rooted binary trees with `n`

leaves.
It is the inverse function of `furnasI()`

. For details on how to calculate
`T`

(including algorithm) 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).

`furnasI_inv`

can be used e.g. to generate random rooted binary trees with a
certain number of leaves. Also, 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_inv(rank, n)
```

`rank` |
An integer denoting the rank of the sought tree among all rooted
binary trees with |

`n` |
An integer denoting the number of leaves of the sought tree. |

`furnasI_inv`

returns the unique tree (in phylo format) for
the given leaf number and rank.

Sophie Kersting

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.

```
furnasI_inv(rank=6,n=8)
```

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