A characterization of collections of two-point sets with the uniqueness property (Q2495301)

The main theorem is: Let \(\{S_1,\dots, S_q\}\) be a collection of pairwise disjoint two-point sets with \(S_j= \{\alpha_j,\beta_j\}\). If \(q\geq 6\), and there is no Möbius transformation \(T\) such that \(T(\alpha_j)=\beta_j\) and \(T(\beta_j)= \alpha_j\) for three distinct \(j\)'s, then the collection of sets has the uniqueness property for meromorphic functions. A similar theorem is proved for entire functions.