Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4650212 | Discrete Mathematics | 2009 | 24 Pages |
Abstract
We analyse qq-functional equations arising from tree-like combinatorial structures, which are counted by size, internal path length, and certain generalisations thereof. The corresponding counting parameters are labelled by a positive integer kk. We show the existence of a joint limit distribution for these parameters in the limit of infinite size, if the size generating function has a square root as dominant singularity. The limit distribution coincides with that of integrals of kkth powers of the standard Brownian excursion. Our approach yields a recursion for the moments of the limit distribution. It can be used to analyse asymptotic expansions of the moments, and it admits an extension to other types of singularity.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Christoph Richard,