On simple arrangements of lines and pseudo-lines in P^2 and R^2 with the maximum number of triangles

TL;DR

This paper explores the maximum number of triangles formed in simple arrangements of lines and pseudo-lines in two-dimensional and projective planes, providing new theoretical bounds and insights.

Contribution

It introduces new bounds and methods for counting triangles in arrangements of lines and pseudo-lines, advancing the understanding of their combinatorial properties.

Findings

Established new upper bounds for the number of triangles

Identified configurations that maximize triangle counts

Extended results to pseudo-line arrangements

Abstract

We give some new advances in the research of the maximum number of triangles that we may obtain in a simple arrangements of n lines or pseudo-lines.