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arXiv 1408.3501math.COmath.GT
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多个三角形奇数球

Many triangulated odd-spheres

Eran Nevo, Francisco Santos, Stedman Wilson

备注：
This paper extends and subsumes arXiv:1311.1641, by two of the authors
发表信息：
Math. Annalen 364:3 (2016), 737-762
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摘要：

已知对于每个$k\ge 2$，$(2k-1)$球至多具有与$n$顶点组合不同的$2^{O(n^k \log n)}$三角剖分.在这里，我们构建至少$2^{Ω(n^k)}$这样的三角形，改进以前的建设，使$2^{Ω(n^{k-1})}$在一般情况下（卡莱）和$2^{Ω(n^{5/4})}$的$k=2$（Pfeifle-Ziegler）。我们还构造了$2^{Ω\left(n^{k-1+\frac{1}{k}}\right)}$测地线（a.k.a.星形凸）$n$-$(2k-1)$ -球面的顶点三角形。作为一个步骤（在$k=2$的情况下），我们构建$n$ -顶点$4$ -多面体包含$Ω(n^{3/2})$小平面，这些小平面不是单纯形，或者具有三度的$Ω(n^{3/2})$边。

英文摘要：

It is known that the $(2k-1)$-sphere has at most $2^{O(n^k \log n)}$ combinatorially distinct triangulations with $n$ vertices, for every $k\ge 2$. Here we construct at least $2^{Ω(n^k)}$ such triangulations, improving on the previous constructions which gave $2^{Ω(n^{k-1})}$ in the general case (Kalai) and $2^{Ω(n^{5/4})}$ for $k=2$ (Pfeifle-Ziegler). We also construct $2^{Ω\left(n^{k-1+\frac{1}{k}}\right)}$ geodesic (a.k.a. star-convex) $n$-vertex triangualtions of the $(2k-1)$-sphere. As a step for this (in the case $k=2$) we construct $n$-vertex $4$-polytopes containing $Ω(n^{3/2})$ facets that are not simplices, or with $Ω(n^{3/2})$ edges of degree three.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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