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Extremal Statistics on Non-Crossing Configurations

Anna De Mier 1 Marc Noy 1 
1 Departament de Matemàtica Aplicada II
UPC - Universitat Politècnica de Catalunya [Barcelona]
Abstract : 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.
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Anna De Mier, Marc Noy. Extremal Statistics on Non-Crossing Configurations. 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), 2012, Nagoya, Japan. pp.631-642, ⟨10.46298/dmtcs.3069⟩. ⟨hal-01283098⟩

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