Description Usage Arguments Value Author(s) References Examples

This function calculates the Colijn-Plazzotta rank *CP(T)* for a
given rooted tree *T*.

For a binary tree *T*, the Colijn-Plazzotta rank *CP(T)* is
recursively defined as *CP(T)=1* if *T* consists of only
one leaf and otherwise

*CP(T)=1/2*CP(T1)(CP(T1)-1)+CP(T2)+1*

with *CP(T1)>=CP(T2)* being the ranks of the two pending
subtrees rooted at the children of the root of *T*. This rank
of *T* corresponds to its position in the
lexicographically sorted list of (*i,j*): (1),(1,1),(2,1),(2,2),(3,1),...
The Colijn-Plazzotta rank of binary trees has been shown to be an imbalance index.

For an arbitrary tree *T* whose maximal number of children of any vertex is *l*,
the Colijn-Plazzotta rank *CP(T)* is recursively defined as *CP(T)=0*
if *T* is the empty tree (with no vertices), *CP(T)=1* if *T* consists
of only one leaf and otherwise *CP(T)=ā_{i=1,...,l} binom{CP(T_i)+i-1,i}*
(with *CP(T_1)<=...<=CP(T_l)*). If there are only *k<l* pending subtrees
rooted at the children of the root of *T*, then *T_1,...,T_{l-k}* are empty trees,
i.e. *CP(T_1)=...=CP(T_{l-k})=0*, and *CP(T_{l-k+1}),...,CP(T_l)* are the
increasingly ordered *CP*-ranks of the *k* pending subtrees rooted at the
children of the root of *T*. Note that if *k=l* there are no empty trees.

For *n=1* the function returns *CP(T)=1* and a warning.

Note that problems can sometimes arise even for trees with small leaf numbers due
to the limited range of computable values (ranks can reach INF quickly).

1 | ```
colPlaLab(tree, method)
``` |

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

`method` |
The method must be one of: "binary" or "arbitrary". Note that (only) in the arbitrary case vertices of out-degree 1 are allowed. |

`colPlaLab`

returns the Colijn-Plazotta rank of the given tree
according to the chosen method.

Sophie Kersting, Luise Kuehn

C. Colijn and G. Plazzotta. A Metric on Phylogenetic Tree Shapes. Systematic Biology, doi: 10.1093/sysbio/syx046.

N. A. Rosenberg. On the Colijn-Plazzotta numbering scheme for unlabeled binary rooted trees. Discrete Applied Mathematics, 2021. doi: 10.1016/j.dam.2020.11.021.

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