Summary: A central approach to bound the number of
crossings in a generalized configuration.
Bernardo M. ´Abrego
Silvia Fern´andez­Merchant
Department of Mathematics, California State University at Northridge
Jes´us Lea~nos
Gelasio Salazar
Instituto de F´isica, Universidad Aut´onoma de San Luis Potos´i, M´exico
Abstract
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 .
Keywords: k-sets, k-sets, rectilinear crossing number, pseudolinear crossing

Source: Abrego, Bernardo - Department of Mathematics, California State University, Northridge
Fernandez, Silvia - Department of Mathematics, California State University, Northridge

Collections: Mathematics