Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 41, No. 1, pp. 181-193 (2000)

The Concept of Cutting Vectors for Vector Systems in the Euclidean Plane

Günter Heinz

Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany

Abstract: The concept of cutting vectors is introduced to study the combinatorial structure of vector configurations in the plane. We give a full characterization of those $n$-tuples of integers which are realizable as cutting vector. Furthermore, "simple" mappings are defined that transform cutting vectors into each other. Thus it becomes possible to consider all combinatorial types of vector systems.

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