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