Dec. 4, 2012, 7:10 a.m. by Rosalind Team

**Topics**:
Combinatorics,
Phylogeny

## Introduction to Quartet-Based Phylogeny

In “Quartets”, we introduced partial splits modeling partial characters on a collection of taxa. Our aim is to use the quartets inferred from partial splits to construct a phylogeny on the taxa. This procedure is called quartet-based phylogeny.

We could construct a phylogeny directly from a collection of partial splits, but it is not immediately clear how many different splits we would need. Hence, our first question is to ask how many quartets are required to be able to infer a tree; in this problem we will ask the reverse question of how many quartets can be inferred from a known tree.

A quartet

Let

Given: A positive integer

Return: The value of

6 (lobster,(cat,dog),(caterpillar,(elephant,mouse)));

15