Pyramidal width of polytopes can increase under vertex insertion, new paper shows

A new paper published on arXiv presents a counterexample to a 2015 conjecture regarding the pyramidal width of polytopes. The research demonstrates that adding a vertex to a polytope can, under certain conditions, increase its pyramidal width. The paper provides a specific instance in 3D space with six integer points, showing that the pyramidal width squared increased from 48/353 to 36/133 after vertex insertion. The proof relies on the equivalence between pyramidal width and facial distance, with all calculations certified by integer supporting hyperplanes. AI

IMPACT This research contributes to theoretical computer science and geometry, with potential indirect implications for optimization algorithms used in AI.

RANK_REASON The cluster contains a peer-reviewed academic paper published on arXiv. [lever_c_demoted from research: ic=1 ai=0.1]

Read on arXiv cs.LG →

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• Lacoste-Julien
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• Pyramidal Width
• Rodalies Barcelona line R3
• v1
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• Vertex insertion approximates the crossing number of apex graphs
• Vha100-1

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