论文标题
动机阐述了特维尔伯格定理的证据
Motivated exposition of the proof of the Tverberg Theorem
论文作者
论文摘要
我们提出了以下tverberg定理证明的动机阐述：对于每个整数$ d，r $任何$ $（d+1）（r-1）（r-1）+1 $点$ \ Mathbb r^d $都可以分解为$ r $ $组，以使所有$ r $ r $ r $ convex hulls hulls的hulls的hulls hulls of toction comporion comporion comporion。证明是通过众所周知的Bárány定理减少。但是，我们的说明更容易掌握，因为其他构造（嵌入$ \ mathbb r^d \ subset \ mathbb r^{d+1} $，vectors $φ_{j，i} $ and i} $和barańytheorem theorem的说明）并未在非动力的方式中介绍，但自然而然地构造了decounds oild offect decound offect decound decound offect。这种尝试是基于将向量之间的几个平等重写为更高维的向量之间的一个平等。
We present a motivated exposition of the proof of the following Tverberg Theorem: For every integers $d,r$ any $(d+1)(r-1)+1$ points in $\mathbb R^d$ can be decomposed into $r$ groups such that all the $r$ convex hulls of the groups have a common point. The proof is by well-known reduction to the Bárány Theorem. However, our exposition is easier to grasp because additional constructions (of an embedding $\mathbb R^d\subset\mathbb R^{d+1}$, of vectors $φ_{j,i}$ and statement of the Barańy Theorem) are not introduced in advance in a non-motivated way, but naturally appear in an attempt to construct the required decomposition. This attempt is based on rewriting several equalities between vectors as one equality between vectors of higher dimension.
