## Mier, Anna, and Noy, Marc - Extremal Statistics on Non-Crossing Configurations

dmtcs:3069 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Extremal Statistics on Non-Crossing Configurations

Authors: Mier, Anna, and Noy, Marc

We obtain several properties of extremal statistics in non-crossing configurations with n vertices. We prove that the maximum degree and the largest component are of logarithmic order, and the diameter is of order $\sqrt{n}$. The proofs are based on singularity analysis, an application of the first and second moment method and on the analysis of iterated functions.

Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Submitted on: January 31, 2017
Keywords: Diameter.,Non-crossing configuration, Extremal parameters, Maximum degree,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]