A central approach to bound the number of crossings in a generalized configuration

A generalized configuration is a set of n points and n 2 pseudolines such that each pseudoline passes through exactly two points, two pseudolines intersect exactly once, and no three pseudolines are concurrent. Following the approach of allowable sequences we prove a recursive inequality for the number of ( k)-sets for generalized configurations. As a consequence we improve the previously best known lower bound on the pseudolinear and rectilinear crossing numbers from 0.37968 n 4 + n3 to 0.379972 n 4 + n3 .

• Type: Journal
• Year: 2008
• Where: ENDM
• Authors: Bernardo M. Ábrego, Silvia Fernández-Merchant, Jesús Leaños, Gelasio Salazar
• Keywords: Allowable Sequences, ENDM 2008, Generalized Configurations, Recursive Inequality