2021/10/15 by Tristram Bogart, Bogart, Tristram, João Gouveia +3
Computer Science · Engineering · #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Packing Problems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2110.08158
openalex publication_date 2021/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The extension complexity of a polytope measures its amenability to succinct representations via lifts. There are several versions of extension complexity, including linear, real semidefinite, and complex semidefinite. We focus on the last of these, for which the least is known, and in particular on understanding which polytopes are complex psd-minimal. We prove the existence of an obstruction to complex psd-minimality which is efficiently computable via lattice membership problems. Using this tool, we complete the classification of complex psd-minimal polygons (geometrically as well as combinatorially). In dimension three we exhibit several new examples of complex psd-minimal polytopes and apply our obstruction to rule out many others.