• Computer Science > Artificial Intelligence Title:Improved Upper Bounds for Slicing the Hypercube Submission history Access Paper: View PDF HTML (experimental) TeX Source References & Citations NASA ADS Google Scholar Semantic Scholar BibTeX formatted citation Bookmark Bibliographic and Citation Tools Code, Data and Media Associated with this Article Demos Recommenders and Search Tools Author Venue Institution Topic arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. • Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. • arXiv is committed to these values and only works with partners that adhere to them. • Have an idea for a project that will add value for arXiv’s community?Learn more about arXivLabs.
Article Summaries:
- Researchers have tightened the theoretical limits for slicing all edges of an n‑dimensional hypercube with hyperplanes. Defining S(n) as the minimum number of hyperplanes required, the new study proves S(n) ≤ ⌈4n/5⌉ for all n, except when n is an odd multiple of 5, where S(n) ≤ 4n/5 + 1. This improves on Paterson’s 1971 bound of ⌈5n/6⌉. The authors also establish stronger lower bounds on the number of edges that can be sliced using fewer than n hyperplanes. The key construction-eight hyperplanes slicing Q₁₀-was discovered with the help of the CPro1 automated reasoning tool.
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