Towards a statement of the S-adic conjecture through examples
  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 factor 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 $C$". 
Fabien Durand (LAMFA), Julien Leroy (LAMFA), Gw\'ena\"el Richomme   (LIRMM)
cs.DM math.CO