On q-functional equations and excursion moments
| dc.creator | Richard, Christoph | |
| dc.date | 2005-03-10 | |
| dc.date | 2007-09-24 | |
| dc.date.accessioned | 2026-07-07T12:08:22Z | |
| dc.date.available | 2026-07-07T12:08:22Z | |
| dc.description | 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. | |
| dc.description | 35 pages, 1 figure. New introduction, typographical errors corrected | |
| dc.identifier | https://arxiv.org/abs/math/0503198 | |
| dc.identifier | http://arxiv.org/abs/math/0503198 | |
| dc.identifier | Discrete Mathematics 309 (2009) 207-230 | |
| dc.identifier | doi:10.1016/j.disc.2007.12.072 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209294 | |
| dc.subject | Combinatorics | |
| dc.subject | Probability | |
| dc.subject | 05A15, 39A13, 60C05,82B41 | |
| dc.title | On q-functional equations and excursion moments | |
| dc.type | text |