Extremal statistics on non-crossing configurations
نویسندگان
چکیده
منابع مشابه
Extremal statistics on non-crossing configurations
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 meth...
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Four statistics, ls, rb, rs, and lb, previously studied on all partitions of { 1, 2, ..., n }, are applied to non-crossing partitions. We consider single and joint distributions of these statistics and prove equidistribution results. We obtain qand p, q-analogues of Catalan and Narayana numbers which refine the rank symmetry and unimodality of the lattice of non-crossing partitions. Two unimoda...
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Article history: Received 9 October 2013 Available online xxxx
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2014
ISSN: 0012-365X
DOI: 10.1016/j.disc.2014.03.016