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Workshop

Sweeps of a point configuration

  • Eva Philippe (Ecole Normale Supérieure de Paris, Paris, France)
Live Stream MPI für Mathematik in den Naturwissenschaften Leipzig (Live Stream)

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.

Links

conference
4/6/21 4/9/21

(Polytop)ics: Recent advances on polytopes

MPI für Mathematik in den Naturwissenschaften Leipzig Live Stream

Saskia Gutzschebauch

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Federico Castillo

Max Planck Institute for Mathematics in the Sciences

Giulia Codenotti

Goethe University Frankfurt

Benjamin Schröter

Royal Institute of Technology (KTH)