Sweeps of a point configuration
- Eva Philippe (Ecole Normale Supérieure de Paris, Paris, France)
Abstract
Consider a configuration of n labeled points in a Euclidean space. Any linear functional gives an ordering of these points: an ordered partition that we call a sweep, because we can imagine its parts as the sets of points successively hit by a sweeping hyperplane. The set of all such sweeps forms a poset which is isomorphic to a polytope, called the sweep polytope.
I will present several constructions of the sweep polytope, related to zonotopes, projections of permutahedra and monotone path polytopes of zonotopes.
This structure can also be generalized in terms of oriented matroids. For oriented matroids that admit a sweep oriented matroid, we gain precision on the topological description of their poset of cellular strings, refining a particular case of the Generalized Baues Problem.
This is joint work with Arnau Padrol.
