Abstract Several typological gaps have attracted a lot of interest in the linguistic literature recently. These concern the Person Case Constraint and the absence of ABA patterns in adjectival gradation, pronoun suppletion, case syncretism, and singular noun allomorphy, among others. This paper is the first to provide a unified explanation of all these phenomena, and it does so via weakly non-inverting graph-transductions. A pattern $P$ is absent from the typology whenever such transductions cannot produce the graph corresponding to $P$ from some fixed underlying base graph. I show that weakly non-inverting graph-transductions are particularly simple from a computational perspective, and consequently all these typological gaps follow from general simplicity desiderata.