Combinatorics of Point Sets and Arrangements of Objects

该CRP主要关注平面上的离散点集和其他简单几何对象的组合特性。一般来说，几何图是离散几何和计算几何的中心主题，数学和计算机科学中的许多重要问题都可以表述为几何图上的问题。我们将研究Erdös-Szekeres-type问题，关于彩色点集的问题，以及关于无交叉构型的计数、枚举和抽样的问题。该方案成员的愿景是作出巨大的共同努力，以便更深入地了解该领域长期存在的问题的结构，并为最终解决这些问题作出重大贡献。

This CRP focuses on combinatorial properties of discrete sets of points and other simple geometric objects primarily in the plane. In general, geometric graphs are a central topic in discrete and computational geometry, and many important questions in mathematics and computer science can be formulated as problems on geometric graphs. We will, among others, investigate Erdös-Szekeres-type problems, questions on colored point sets, and problems on counting, enumerating and sampling of crossing-free configurations. It is the vision of the members of this CRP to make a massive joint effort in order to gain deeper insight into the structure of long-standing problems in the field, and to contribute major steps towards their final solution.