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@article{faucris.120627584,
abstract = {We analyse q$q$-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 k$k$. 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 k$k$th 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.},
author = {Richard, Christoph},
doi = {10.1016/j.disc.2007.12.072},
faupublication = {yes},
journal = {Discrete Mathematics},
keywords = {Simply generated trees; qq-difference equation; Brownian excursion; Limit distribution},
pages = {207--230},
peerreviewed = {Yes},
title = {{On} q-functional equations and excursion moments},
volume = {309},
year = {2009}
}