Highly neighborly centrally symmetric spheres
Highly neighborly centrally symmetric spheres
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DOI：
10.1016/j.aim.2020.107238
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发表时间：
2019-07
影响因子：
1.7
通讯作者：
I. Novik;Hailun Zheng
中科院分区：
文献类型：
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作者：
I. Novik;Hailun Zheng
在1995年，Jockusch构造了一个无限族的中心对称的3维单形球，它们是cs-2-邻域的。在这里我们推广了他的构造，证明了对所有d≥ 3和n≥ d+ 1，存在一个中心对称的2n个顶点的d维单形球面是cs-ε d/2 ε-邻域的.这个结果与Adin和Stanley的工作相结合，完全解决了中心对称单纯球的上界问题。
In 1995, Jockusch constructed an infinite family of centrally symmetric 3-dimensional simplicial spheres that are cs-2-neighborly. Here we generalize his construction and show that for all d≥ 3 and n≥ d+ 1, there exists a centrally symmetric d-dimensional simplicial sphere with 2n vertices that is cs-⌈ d/2⌉-neighborly. This result combined with work of Adin and Stanley completely resolves the upper bound problem for centrally symmetric simplicial spheres.