On the number of increasing trees with label repetitions

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dc.contributor.authorBodini, Olivieren_ZA
dc.contributor.authorGenitrini, Antoineen_ZA
dc.contributor.authorGittenberger, Bernharden_ZA
dc.contributor.authorWagner, Stephanen_ZA
dc.date.accessioned2022-07-01T07:30:06Z
dc.date.available2022-07-01T07:30:06Z
dc.date.issued2019
dc.descriptionCITATION: Bodini, O. et al. 2020. On the number of increasing trees with label repetitions. Discrete Mathematics, 343(8). doi:10.1016/j.disc.2019.111722
dc.descriptionThe original publication is available at https://www.sciencedirect.com/journal/discrete-mathematics
dc.description.abstractWe study the asymptotic number of certain monotonically labeled increasing trees arising from a generalized evolution process. The main difference between the presented model and the classical model of binary increasing trees is that the same label can appear in distinct branches of the tree. In the course of the analysis we develop a method to extract asymptotic information on the coefficients of purely formal power series. The method is based on an approximate Borel transform (or, more generally, Mittag-Leffler transform) which enables us to quickly guess the exponential growth rate. With this guess the sequence is then rescaled and a singularity analysis of the generating function of the scaled counting sequence yields accurate asymptotics. The actual analysis is based on differential equations and a Tauberian argument. The counting problem for trees of size n exhibits interesting asymptotics involving powers of n with irrational exponents.en_ZA
dc.description.urihttps://www.sciencedirect.com/science/article/pii/S0012365X19304005
dc.description.versionPublishers version
dc.format.extent12 pages
dc.identifier.citationBodini, O. et al. 2020. On the number of increasing trees with label repetitions. Discrete Mathematics, 343(8). doi:10.1016/j.disc.2019.111722
dc.identifier.issn0012-365X (print)
dc.identifier.otherdoi:10.1016/j.disc.2019.111722
dc.identifier.urihttp://hdl.handle.net/10019.1/125445
dc.language.isoen_ZAen_ZA
dc.publisherElsevier
dc.subjectIncreasing treeen_ZA
dc.subjectBorel transformen_ZA
dc.subjectEvolution processen_ZA
dc.subjectOrdinary differential equationen_ZA
dc.subjectAsymptotic enumerationen_ZA
dc.subjectTrees -- Labelingen_ZA
dc.subjectTrees -- Growth -- Mathematical modelsen_ZA
dc.subjectEvolution equations -- Asymptotic theoryen_ZA
dc.titleOn the number of increasing trees with label repetitionsen_ZA
dc.typeArticleen_ZA
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