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Workshop

Generators for type B permutahedra via McMullen's polytope algebra

  • Jose Bastidas (Cornell University, Ithaca, USA)
Live Stream MPI für Mathematik in den Naturwissenschaften Leipzig (Live Stream)

Abstract

Ardila-Benedetti-Doker showed that any generalized permutahedron is a signed Minkowski sum of the faces of the standard simplex. In contrast, Ardila-Castillo-Eur-Postnikov observed that the faces of the cross-polytope only generate a subspace of roughly half the dimension in the space of deformations of the type B permutahedron. In this talk, I will use McMullen's polytope algebra to help explain this phenomenon. Concretely, I will consider the subalgebra generated by (type B) generalized permutahedra and endow it with the structure of a module over the Tits algebra of the corresponding Coxeter arrangement. The module structure surprisingly reveals that any family of generators (via signed Minkowski sums) for generalized permutahedra of type B will contain at least $2^{d-1}$ full-dimensional polytopes. I will present a family of generators that shows that this lower bound is sharp.

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)