In this note we apply a substantial improvement of a result of S. Ferenczi on $S$-adic subshifts to give Bratteli-Vershik representations of these subshifts.
The $S$-adic conjecture claims that there exists a condition $C$ such that a sequence has a sub-linear complexity if and only if it is an $S$-adic sequence satisfying Condition $C$ for some finite set $S$ of morphisms. We present an overview of the f
actor complexity of $S$-adic sequences and we give some examples that either illustrate some interesting properties or that are counter-examples to what could be believed to be a good Condition $C$.
