Plane recursive trees, Stirling permutations and an urn model

2008/03/07 by Svante Janson, Janson, Svante · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #math.CO #math.PR

paper · pdf · doi:10.48550/arxiv.0803.1129

8 pages

arxiv created 2008/03/07 · openalex publication_date 2008/03/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We exploit a bijection between plane recursive trees and Stirling permutations; this yields the equivalence of some results previously proven separately by different methods for the two types of objects as well as some new results. We also prove results on the joint distribution of the numbers of ascents, descents and plateaux in a random Stirling permutation. The proof uses an interesting generalized Polya urn

Citations

• Embedding of Urn Schemes into Continuous Time Markov Branching Processes and Related Limit Theorems

Cited by

• Labeled Plane Trees and Increasing Plane Trees

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