A character is some feature, either physical or genetic, that divides a collection of
taxa into two groups. The ultimate goal is to apply characters to the
construction of a phylogeny, where taxa are represented as the leaves of a tree.
There are two common ways of encoding a given character $C$ dividing a collection of $n$ taxa.
$C$ can be written in split notation as $S \mid S^{\textrm{c}}$, where $S$ is a subset
of our taxa and $S^{\textrm{c}}$ is the set complement of $S$.
Removing an edge from a tree divides its leaves into two disjoint sets$S$ and
$S^{\textrm{c}}$, so that we can establish a correspondence between characters and edges
of the phylogeny: specifically, we may assign each character to the edge that
its split notation implies.
The second notation for $C$ assumes that we have ordered our $n$ taxa,
after which $C$ may be written in array notation as an array $A$ in which $A[i]$ is
equal to 1 or 0 depending on whether the $i$th taxon belongs to $S$ or $S^{\textrm{c}}$.
Given a collection of arrays from a number of different characters, we may
combine the arrays into a matrix called a character table. The creation of
a phylogeny from a character table is an important algorithmic problem.
