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.
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.
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.
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