Scripts and data associated to the paper "On Sackin's original proposal: The variance of the leaves' depths as a phylogenetic balance index".

It contains the following R Mardown files:

• Figure11.Rmd: Produces Figure 11 in the main text
• Figure12.Rmd: Produces Figure 11 in the main text
• MinVar.Rmd: Illustrates the function MinVar to compute the minimum value of $V$ for trees with $n$ leaves and the multiset(s) of depths of the tree(s) achieving it.
• Lists_of_MinVar.Rmd: Computes the tables in folder Tables
• UniqueMinima.Rmd: Checks the uniqueness of the type of trees achieving the minimum $V$ value for $n$ up to 2^20^

It also contains the HTML files obtained knitting them.

Python script defining the functions

• var_depths: that computes the variance of the leaves' depths of a given tree
• max_var_depths: that returns the tuple formed by the maximum variance of a given number of leaves and the only tree that attains it
• min_var_depths: that returns the tuple formed by the minimum variance of a given number of leaves and ONE tree that attains it
• min_var_depths_vector: that returns the tuple formed by the minimal variance of a given number of leaves and the vector of l_i's

It contains the types of trees with minimum V value for n from 2^8^ to 2^20^. Each file Resultsk_k+1.txt contains the results from 2^k^to 2^k+1^. The last file, from 2^19^ to 2^20^, is split into two files.

It contains the R Markdown file, and the data files generated and used by it, used in the computations yielding Table 3 in the main text