A configuration space models $n$ particles existing in a topological space $X$ with no collisions allowed. There have been many variations on these spaces, such as the “no-$k$-equal” type where collisions of fewer than $k$ particles are allowed. In this talk, we introduce a generalization where collisions are allowed or disallowed based on partitions of the $n$ particles. Depending on which partitions are disallowed, this framework yields many of the previously considered types of configuration spaces as well as new types. We also discuss the case where the space $X$ is a graph and provide discrete models for its forbidden partition configuration spaces.

This talk is based on a paper “Forbidden partition configuration spaces of graphs” (J. Dover) which has been accepted for publication in the Bulletin of the Australian Mathematical Society.