On q-functional equations and excursion moments

Details On q-functional equations and excursion moments On q-functional equations and excursion moments

2005-03-10

arxiv.org/abs/math/0503198v2

Discrete Mathematics 309 (2009) 207-230

Mathematics

Combinatorics

35 pages, 1 figure. New introduction, typographical errors corrected

Scientific paper

10.1016/j.disc.2007.12.072

We analyse 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. 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-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.

Affiliated with

Also associated with

No associations

Rating

On q-functional equations and excursion moments does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On q-functional equations and excursion moments, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On q-functional equations and excursion moments will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-685528