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

نویسندگان

  • Bernardo M. Ábrego
  • Silvia Fernández-Merchant
  • Jesús Leaños
  • Gelasio Salazar
چکیده

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 ) + Θ ( n 3 ) to 0.379972 ( n 4 ) +Θ ( n 3 ) .

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عنوان ژورنال:
  • Electronic Notes in Discrete Mathematics

دوره 30  شماره 

صفحات  -

تاریخ انتشار 2008