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math.CO2023
The Best Ways to Slice a Polytope
Marie-Charlotte Brandenburg, Jesús A. De Loera, Chiara Meroni
We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane a…
math.MG2023
Intersection Bodies of Polytopes: Translations and Convexity
Marie-Charlotte Brandenburg, Chiara Meroni
We continue the study of intersection bodies of polytopes, focusing on the behavior of under translations of . We introduce an affine hyperplane arrangement and show that t…