Happy Ending or Many Concurrent Lines

2024/09/04 by Furukawa, Koki
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.03122

Abstract

For each n ≥ 2, l ≥ 3, let ES_L (l,n) be the minimum N such that every family of N-lines in the plane contains either l concurrent lines or n lines in convex position. In this papar, we give the upper and lower bounds for ES_L (l,n). This is one of the extensions of the line version of Erdös-Szekeres convex polygon problem.

Related

• Erdős - Szekeres Theorem for Lines
• On the Erdos-Szekeres convex polygon problem
• Big line or big convex polygon
• Big convex polytopes or rich hyperplanes
• Balanced convex partitions of lines in the plane