par Fiorini, Samuel ;Fisikopoulos, Vissarion ;Macchia, Marco
Référence Lecture notes in computer science, 9849 LNCS, page (285-296)
Publication Publié, 2016
Article révisé par les pairs
Résumé : A (convex) polytope is said to be 2-level if for every facetdefining direction of hyperplanes, its vertices can be covered with two hyperplanes of that direction. These polytopes are motivated by questions, e.g., in combinatorial optimization and communication complexity. We study 2-level polytopes with one prescribed facet. Based on new general findings about the structure of 2-level polytopes, we give a complete characterization of the 2-level polytopes with some facet isomorphic to a sequentially Hanner polytope, and improve the enumeration algorithm of Bohn et al. (ESA 2015). We obtain, for the first time, the complete list of d-dimensional 2-level polytopes up to affine equivalence for dimension d = 7. As it turns out, geometric constructions that we call suspensions play a prominent role in both our theoretical and experimental results. This yields exciting new research questions on 2-level polytopes, which we state in the paper.