Abstract
In this paper, we first study clusters in type (A) over cap by collecting them into a finite number of infinite families given by Dehn twists of their corresponding triangulations, and show that these families are counted by the Catalan numbers. We also highlight the similarities and differences between the annuli diagrams used to study clusters and those used to study exceptional sets in type (A) over cap. We then focus on exceptional collections (sets) of modules over path algebras of quivers by first showing that the notion of relative projectivity in exceptional sets is well defined. We finish by counting the number of exceptional sets of representations of type Lambda quivers with straight orientation and using this to count the number of families of exceptional sets of type (A) over cap with straight orientation.