Extremal statistics on non-crossing configurations
نویسندگان
چکیده
We analyze extremal statistics in non-crossing configurations on the n vertices of a convex polygon.We prove that themaximumdegree 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 √ n. The proofs are based on singularity analysis, an application of the first and second moment method, and on the analysis of iterated functions. © 2014 Elsevier B.V. All rights reserved.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 327 شماره
صفحات -
تاریخ انتشار 2014