English(EN) Pyramidal Width Can Increase Under Vertex Insertion

新论文显示，多面体的锥形宽度在顶点插入时可以增加

作者 PulseAugur 编辑部 · [1 个来源] · 2026-08-03 04:00

一篇新发表在arXiv上的论文提出了一个反例，反驳了2015年关于多面体锥形宽度的猜想。研究表明，在某些条件下，向多面体添加一个顶点可以增加其锥形宽度。该论文提供了一个在3D空间中的具体实例，包含六个整数点，显示在顶点插入后，锥形宽度平方从48/353增加到36/133。证明依赖于锥形宽度与面距离之间的等价性，所有计算均由整数支撑超平面认证。 AI

影响这项研究为理论计算机科学和几何学做出了贡献，可能对AI中使用的优化算法产生间接影响。

排序理由该集群包含一篇在arXiv上发表的同行评审学术论文。[lever_c_demoted from research: ic=1 ai=0.1]

在 arXiv cs.LG 阅读 →

AI 生成摘要 · Google Gemini · 来自 1 个来源。我们如何撰写摘要 →

本文如何被排名

Signal score: 0 / 100; Composite score across the factors below. Higher = stronger signal that this story matters right now.
Newsworthiness bucket: Tool; 该集群包含一篇在arXiv上发表的同行评审学术论文。[lever_c_demoted from research: ic=1 ai=0.1]
Source corroboration: Single-source cluster; Only one publisher covered this so far. Single-source stories can still rank when the publisher is high-authority, but they lack cross-source corroboration.
Topics: paper, other; Editorial topic classification. Feeds into how the story surfaces on /topic/<slug> hub pages and into the per-entity coverage mix.
AI-industry relevance: Low; Off-topic or adjacent — cluster remains reachable but doesn't surface in AI-industry rankings.
Story freshness: 51 days old; Aged out of breaking-news scoring windows; ranking reflects the durable signal from the full source set.

完整方法见我们的编辑标准。

报道来源 [1]

arXiv cs.LG TIER_1 English(EN) · Jinze Zhao · 2026-08-03 04:00

顶点插入可增加金字塔宽度

arXiv:2607.29555v1 Announce Type: new Abstract: Lacoste-Julien and Jaggi conjectured in 2015 that the pyramidal width of a polytope cannot increase when a vertex is added, provided that every old point remains a vertex. We give an exact counterexample with six integer points in $…

本文如何被排名

报道来源 [1]

顶点插入可增加金字塔宽度

相关实体

相关话题