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Extremal statistics on non-crossing configurations

Autor
Drmota, M.; De Mier, A.; Noy, M.
Tipus d'activitat
Article en revista
Revista
Discrete mathematics
Data de publicació
2014-07-28
Volum
327
Pàgina inicial
103
Pàgina final
117
DOI
https://doi.org/10.1016/j.disc.2014.03.016 Obrir en finestra nova
Projecte finançador
Combinatoria, teoría de grafos y geometría discreta
URL
http://dx.doi.org/10.1016/j.disc.2014.03.016 Obrir en finestra nova
Resum
We analyze extremal statistics in non-crossing configurations on the n vertices of a convex polygon. We prove that the maximum degree and the largest component are of logarithmic order, and that, suitably scaled, they converge to a well-defined constant. We also prove that the diameter is of order root n. The proofs are based on singularity analysis, an application of the first and second moment method, and on the analysis of iterated functions. (C) 2014 Elsevier B.V. All rights reserved.
Paraules clau
Analytic combinatorics, BINARY-TREES, DIAMETER, Extremal parameter, GRAPHS, HEIGHT, Noncrossing configuration, TRIANGULATIONS
Grup de recerca
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

Participants