  Diversity plays a crucial role in multiple contexts such as team formation,
representation of minority groups and generally when allocating resources
fairly. Given a community composed by individuals of different types, we study
the problem of partitioning this community such that the global diversity is
preserved as much as possible in each subgroup. We consider the diversity
metric introduced by Simpson in his influential work that, roughly speaking,
corresponds to the inverse probability that two individuals are from the same
type when taken uniformly at random, with replacement, from the community of
interest. We provide a novel perspective by reinterpreting this quantity in
geometric terms. We characterize the instances in which the optimal partition
exactly preserves the global diversity in each subgroup. When this is not
possible, we provide an efficient polynomial-time algorithm that outputs an
optimal partition for the problem with two types. Finally, we discuss further
challenges and open questions for the problem that considers more than two
types.

Discrete Mathematics;Data Structures and Algorithms