Jacob E. Goodman

TL;DR: In this paper, the authors present a collection of 32 papers on a broad range of topics of current interest in the field, including geometric arrangements, polytopes, packing, covering, discrete convexity, geometric algorithms and their complexity, and combinatorial complexity of geometric objects, particularly in low dimension.

TL;DR: Theorem 1.1 (Helly's Theorem) of transversal theory has its origins in Helly's theorem as mentioned in this paper, which states that if every d + 1 members of a convex set have a common point, then there is a point common to all the members of the set.

TL;DR: On montre que l'equivalence de semi-espace est la notion appropriee pour distinguer les proprietes des configurations qui se relient a l'orientation, the separation and the convexite.

TL;DR: It is proved that for n ⩽ 5 every sequence essentially distinct from this one is realized geometrically by giving a complete classification of configurations by developing some basic notions of the geometry of “allowable sequences” in the course of proving this classification theorem.