A partition is a finite sequence of positive integers. The Plancherel (probability) measure on the set of partitions comes from the representation theory of the symmetric group. We will introduce two aspects of partition theory: the fact that a certain associated process on $\mathbb{Z}$ is determinantal under the Plancherel measure, and the (representation-theoretic) notion of core of a partition. We will then show how to obtain the asymptotic size of the core of a partition under the Plancherel measure.