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Plus Minus Analogues for Affine Tverberg Type Results
Discrete & Computational Geometry ( IF 0.8 ) Pub Date : 2019-08-01 , DOI: 10.1007/s00454-019-00120-y
Pavle V. M. Blagojević , Günter M. Ziegler

The classical 1966 theorem of Tverberg with its numerous variations was and still is a motivating force behind many important developments in convex and computational geometry as well as a testing ground for methods from equivariant algebraic topology. In 2018, Bárány and Soberón presented a new variation, the “Tverberg plus minus theorem.” In this paper, we give a new proof of the Tverberg plus minus theorem, by using a projective transformation. The same tool allows us to derive plus minus analogues of all known affine Tverberg type results. In particular, we prove a plus minus analogue of the optimal colored Tverberg theorem.

中文翻译:

Affine Tverberg 类型结果的加减类似物

1966 年的经典 Tverberg 定理及其众多变体曾经是并且仍然是凸几何和计算几何许多重要发展背后的推动力,也是等变代数拓扑方法的试验场。2018 年,Bárány 和 Soberón 提出了一个新的变体,即“Tverberg 正负定理”。在本文中,我们通过使用投影变换给出了 Tverberg 正负定理的新证明。相同的工具允许我们推导出所有已知仿射 Tverberg 类型结果的正负类似物。特别是,我们证明了最佳有色 Tverberg 定理的正负模拟。
更新日期:2019-08-01
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