Eva Philippe:Sweep polytopes and sweep oriented matroids

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.

Zoom meeting ID: 654 5562 3260

Zoom link: https://kth-se.zoom.us/j/65455623260