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Limit shapes are an increasingly popular way to understand the large-scale characteristics of a random ensemble. The limit shape of unrestricted integer partitions has been studied by many authors primarily under the uniform measure and Plancherel measure. In addition, asymptotic properties of integer partitions subject to restrictions has also been studied, but mostly with respect to independent conditions of the form "parts of size i can occur at most a_i times." While there has been some progress on asymptotic properties of integer partitions under other types of restrictions, the techniques are mostly ad hoc. In this talk, we will present an approach to finding limit shapes of restricted integer partitions which extends the types of restrictions currently available, using classes of asymptotically stable bijections. This is joint work with Igor Pak.