Combinatorics of free and simplicial line arrangements

2018/09/25 by David Geis, Geis, David
Mathematics · #52C30 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1809.09362

openalex publication_date 2018/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the combinatorics of pseudoline arrangements in the real projective plane. Our focus lies on two classes of arrangements: simplicial arrangements and arrangements whose characteristic polynomials have only real roots. We derive inequalities involving the t-vectors of the arrangements in consideration. As application, we obtain some finiteness and classification results. Moreover, we are able to prove the Dirac Motzkin Conjecture for real pseudoline arrangements whose charateristic polynomials split over ℝ.

Citations

• On the Number of Ordinary Lines Determined by n Points

Related

• Simplicial arrangements with up to 27 lines
• On free line arrangements with double, triple and quadruple points
• On simplicial arrangements in ℙ³(ℝ) with splitting polynomial
• Topology and combinatorics of real line arrangements
• Combinatorial simpliciality of arrangements of hyperplanes