furnasI_inv: Calculation of rooted binary tree for tuple (rank, leaf...
In treebalance: Computation of Tree (Im)Balance Indices

Description Usage Arguments Value Author(s) References Examples

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. (2021).

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.

1	furnasI_inv(rank, n)

`rank`	An integer denoting the rank of the sought tree among all rooted binary trees with n leaves.
`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.