论文标题
彩色单词和D-Tverberg综合体
Colorful Words and d-Tverberg Complexes
论文作者
论文摘要
我们给出了弱$ d $ -tverberg综合体的完整组合表征。这些复合物记录了凸壳的相交组合物的相交组合必然会以$ \ Mathbb r^d $设置的任何足够大的一般位置点出现。这加强了$ d $代表性的复合物的概念，该复合物描述了至少在一个点集中出现的交叉组合。我们的表征使我们可以为每张固定的$ d $一个图构造，这些图并非$ d'$ - tverberg对于任何$ d'\ le d $，回答了de loera，hogan，oliveros和yang的问题。
We give a complete combinatorial characterization of weakly $d$-Tverberg complexes. These complexes record which intersection combinatorics of convex hulls necessarily arise in any sufficiently large general position point set in $\mathbb R^d$. This strengthens the concept of $d$-representable complexes, which describe intersection combinatorics that arise in at least one point set. Our characterization allows us to construct for every fixed $d$ a graph that is not weakly $d'$-Tverberg for any $d'\le d$, answering a question of De Loera, Hogan, Oliveros, and Yang.
