Combinatorics of Point Sets and Arrangements of Objects

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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.