Growing and destroying Catalan–Stanley trees

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dc.contributor.authorHack, Benjaminen_ZA
dc.contributor.authorProdinger, Helmuten_ZA
dc.date.accessioned2019-09-16T08:09:30Z
dc.date.available2019-09-16T08:09:30Z
dc.date.issued2018
dc.descriptionCITATION: Hack, B. & Prodinger, H. 2018. Growing and destroying catalan–stanley trees. Discrete Mathematics and Theoretical Computer Science, 20(1):1-14, doi:10.23638/DMTCS-20-1-11.en_ZA
dc.descriptionThe original publication is available at https://www.semanticscholar.orgen_ZA
dc.description.abstractStanley lists the class of Dyck paths where all returns to the axis are of odd length as one of the many objects enumerated by (shifted) Catalan numbers. By the standard bijection in this context, these special Dyck paths correspond to a class of rooted plane trees, so-called Catalan–Stanley trees. This paper investigates a deterministic growth procedure for these trees by which any Catalan–Stanley tree can be grown from the tree of size one after some number of rounds; a parameter that will be referred to as the age of the tree. Asymptotic analyses are carried out for the age of a random Catalan–Stanley tree of given size as well as for the “speed” of the growth process by comparing the size of a given tree to the size of its ancestors.en_ZA
dc.description.urihttps://www.semanticscholar.org/paper/Growing-and-Destroying-Catalan-Stanley-Trees-Hackl-Prodinger/eced0779211103ebf2752dc775e2a91b5beb5d73
dc.description.versionPublisher's versionen_ZA
dc.format.extent14 pagesen_ZA
dc.identifier.citationHack, B. & Prodinger, H. 2018. Growing and destroying catalan–stanley trees. Discrete Mathematics and Theoretical Computer Science, 20(1):1-14, doi:10.23638/DMTCS-20-1-11en_ZA
dc.identifier.issn1365-8050 (online)
dc.identifier.issn1462-7264 (print)
dc.identifier.otherdoi:10.23638/DMTCS-20-1-11
dc.identifier.urihttp://hdl.handle.net/10019.1/106475
dc.language.isoen_ZAen_ZA
dc.publisherDiscrete Mathematics and Theoretical Computer Scienceen_ZA
dc.rights.holderAuthors retain copyrighten_ZA
dc.subjectPlanar treesen_ZA
dc.subjectCatalan–Stanley treesen_ZA
dc.subjectDyck pathsen_ZA
dc.subjectAsymptotic analysisen_ZA
dc.titleGrowing and destroying Catalan–Stanley treesen_ZA
dc.typeArticleen_ZA
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