arXiv
Open Access
2021
Independent Hyperplanes in Oriented Paving Matroids
Lamar Chidiac
Winfried Hochstättler
Abstrak
In 1993, Csima and Sawyer proved that in a non-pencil arrangement of n pseudolines, there are at least $\frac{6}{13}n$ 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 $r \ge 3$ on $n$ elements, where $n \geq 5+ r$, has at least $\frac{12}{13(r-1)} \binom{n}{r-2}$ independent hyperplanes, yielding a new necessary condition for a paving matroid to be orientable.
Topik & Kata Kunci
Penulis (2)
L
Lamar Chidiac
W
Winfried Hochstättler
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2021
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓