\begin{definition}[Definition:Flat (Matroid)]
Let $M = \struct{S, \mathscr I}$ be a matroid.
Let $\rho : \powerset S \to \Z$ be the rank function of $M$.
 
A subset $A \subseteq S$ is a '''flat''' of $M$ {{iff}}:
:$\forall x \in S \setminus A : \map \rho {A \cup \set x} = \map \rho A + 1$
\end{definition}