2021/01/28 by Lamar Chidiac, Chidiac, Lamar, Winfried Hochstättler +1
Computer Science · Engineering · #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2101.12290
openalex publication_date 2021/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1993, Csima and Sawyer proved that in a non-pencil arrangement of n pseudolines, there are at least (6)/(13)n simple points of intersection. Since pseudoline arrangements are the topological representations of reorientation classes of oriented matroids of rank 3, in this paper, we will use this result to prove by induction that an oriented paving matroid of rank r ≥ 3 on n elements, where n ≥ 5+ r, has at least (12)/(13(r-1)) \binomnr-2 independent hyperplanes, yielding a new necessary condition for a paving matroid to be orientable.